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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 94815f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94815.k2 | 94815f1 | \([1, -1, 1, -377, -24]\) | \(1860867/1075\) | \(3414762225\) | \([2]\) | \(36864\) | \(0.51879\) | \(\Gamma_0(N)\)-optimal |
| 94815.k1 | 94815f2 | \([1, -1, 1, -4052, 99936]\) | \(2315685267/9245\) | \(29366955135\) | \([2]\) | \(73728\) | \(0.86536\) |
Rank
sage: E.rank()
The elliptic curves in class 94815f have rank \(1\).
Complex multiplication
The elliptic curves in class 94815f do not have complex multiplication.Modular form 94815.2.a.f
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.
