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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1088.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1088.a1 | 1088j2 | \([0, 1, 0, -65, -161]\) | \(941192/289\) | \(9469952\) | \([2]\) | \(384\) | \(0.043360\) | |
1088.a2 | 1088j1 | \([0, 1, 0, -25, 39]\) | \(438976/17\) | \(69632\) | \([2]\) | \(192\) | \(-0.30321\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1088.a have rank \(2\).
Complex multiplication
The elliptic curves in class 1088.a do not have complex multiplication.Modular form 1088.2.a.a
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.