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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 350658j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350658.j2 | 350658j1 | \([1, -1, 0, -128928003, -569064978091]\) | \(-183519341483677631433/2132733310124032\) | \(-2754356756444530745131008\) | \([2]\) | \(68812800\) | \(3.5027\) | \(\Gamma_0(N)\)-optimal |
| 350658.j1 | 350658j2 | \([1, -1, 0, -2068567683, -36211495809835]\) | \(757965222323107486686153/100624463099776\) | \(129953270991183155074944\) | \([2]\) | \(137625600\) | \(3.8493\) |
Rank
sage: E.rank()
The elliptic curves in class 350658j have rank \(1\).
Complex multiplication
The elliptic curves in class 350658j do not have complex multiplication.Modular form 350658.2.a.j
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.
