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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 124.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
124.a1 | 124a1 | \([0, 1, 0, -2, 1]\) | \(-87808/31\) | \(-496\) | \([3]\) | \(6\) | \(-0.77176\) | \(\Gamma_0(N)\)-optimal |
124.a2 | 124a2 | \([0, 1, 0, 18, -11]\) | \(38112512/29791\) | \(-476656\) | \([]\) | \(18\) | \(-0.22246\) |
Rank
sage: E.rank()
The elliptic curves in class 124.a have rank \(1\).
Complex multiplication
The elliptic curves in class 124.a do not have complex multiplication.Modular form 124.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.