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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 287300f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 287300.f2 | 287300f1 | \([0, -1, 0, 1972, -9608]\) | \(27440/17\) | \(-525156819200\) | \([]\) | \(168480\) | \(0.93803\) | \(\Gamma_0(N)\)-optimal |
| 287300.f1 | 287300f2 | \([0, -1, 0, -31828, -2253928]\) | \(-115431760/4913\) | \(-151770320748800\) | \([]\) | \(505440\) | \(1.4873\) |
Rank
sage: E.rank()
The elliptic curves in class 287300f have rank \(1\).
Complex multiplication
The elliptic curves in class 287300f do not have complex multiplication.Modular form 287300.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
