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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 116688c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116688.m2 | 116688c1 | \([0, -1, 0, -507, 5070]\) | \(-902576293888/126190779\) | \(-2019052464\) | \([2]\) | \(59392\) | \(0.51688\) | \(\Gamma_0(N)\)-optimal |
| 116688.m1 | 116688c2 | \([0, -1, 0, -8372, 297648]\) | \(253526452425808/4091373\) | \(1047391488\) | \([2]\) | \(118784\) | \(0.86346\) |
Rank
sage: E.rank()
The elliptic curves in class 116688c have rank \(1\).
Complex multiplication
The elliptic curves in class 116688c do not have complex multiplication.Modular form 116688.2.a.c
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 Cremona 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 Cremona labels.
