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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 296208cn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296208.cn1 | 296208cn1 | \([0, 0, 0, -1424775, -653912314]\) | \(967473250000/1153977\) | \(381523029110454528\) | \([2]\) | \(3686400\) | \(2.2847\) | \(\Gamma_0(N)\)-optimal |
| 296208.cn2 | 296208cn2 | \([0, 0, 0, -1054515, -1001734558]\) | \(-98061470500/271048833\) | \(-358452107114834101248\) | \([2]\) | \(7372800\) | \(2.6313\) |
Rank
sage: E.rank()
The elliptic curves in class 296208cn have rank \(1\).
Complex multiplication
The elliptic curves in class 296208cn do not have complex multiplication.Modular form 296208.2.a.cn
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.
