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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 59850.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59850.v1 | 59850e4 | \([1, -1, 0, -197453067, -1067882786659]\) | \(2768241956450868452043/2058557375000\) | \(633102887689453125000\) | \([2]\) | \(8957952\) | \(3.3014\) | |
| 59850.v2 | 59850e3 | \([1, -1, 0, -12260067, -16912511659]\) | \(-662660286993086283/18441985352000\) | \(-5671774963803375000000\) | \([2]\) | \(4478976\) | \(2.9548\) | |
| 59850.v3 | 59850e2 | \([1, -1, 0, -2972067, -775143659]\) | \(6882017790203934867/3366201047283200\) | \(1420116066822600000000\) | \([2]\) | \(2985984\) | \(2.7521\) | |
| 59850.v4 | 59850e1 | \([1, -1, 0, 675933, -92967659]\) | \(80956273702840173/55667967918080\) | \(-23484923965440000000\) | \([2]\) | \(1492992\) | \(2.4055\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59850.v have rank \(0\).
Complex multiplication
The elliptic curves in class 59850.v do not have complex multiplication.Modular form 59850.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
