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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 364140.cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 364140.cg1 | 364140cg2 | \([0, 0, 0, -226287, 40591206]\) | \(10536048/245\) | \(29798257613725440\) | \([2]\) | \(2949120\) | \(1.9470\) | |
| 364140.cg2 | 364140cg1 | \([0, 0, 0, -31212, -1193859]\) | \(442368/175\) | \(1330279357755600\) | \([2]\) | \(1474560\) | \(1.6004\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 364140.cg have rank \(0\).
Complex multiplication
The elliptic curves in class 364140.cg do not have complex multiplication.Modular form 364140.2.a.cg
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 LMFDB 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 LMFDB labels.
