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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 262080z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 262080.z1 | 262080z1 | \([0, 0, 0, -707628, -107860912]\) | \(820221748268836/369468094905\) | \(17651613118348984320\) | \([2]\) | \(4816896\) | \(2.3884\) | \(\Gamma_0(N)\)-optimal |
| 262080.z2 | 262080z2 | \([0, 0, 0, 2456052, -807666928]\) | \(17147425715207422/12872524043925\) | \(-1229988826712811110400\) | \([2]\) | \(9633792\) | \(2.7350\) |
Rank
sage: E.rank()
The elliptic curves in class 262080z have rank \(1\).
Complex multiplication
The elliptic curves in class 262080z do not have complex multiplication.Modular form 262080.2.a.z
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.
