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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 377706v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377706.v1 | 377706v1 | \([1, 1, 0, -635149944, -6025987949760]\) | \(191419196757975012994777/4816668944272195584\) | \(713039869184025931259314176\) | \([2]\) | \(212889600\) | \(3.9356\) | \(\Gamma_0(N)\)-optimal |
| 377706.v2 | 377706v2 | \([1, 1, 0, 101556616, -19177526117568]\) | \(782494606698830369063/1073710038353163337728\) | \(-158947620055834630662771720192\) | \([2]\) | \(425779200\) | \(4.2822\) |
Rank
sage: E.rank()
The elliptic curves in class 377706v have rank \(1\).
Complex multiplication
The elliptic curves in class 377706v do not have complex multiplication.Modular form 377706.2.a.v
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.
