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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 154800.cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154800.cg1 | 154800ee2 | \([0, 0, 0, -3948675, -2764410750]\) | \(3940344055317123/369800000000\) | \(639014400000000000000\) | \([2]\) | \(5308416\) | \(2.7305\) | |
| 154800.cg2 | 154800ee1 | \([0, 0, 0, -876675, 267653250]\) | \(43121696645763/7045120000\) | \(12173967360000000000\) | \([2]\) | \(2654208\) | \(2.3839\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 154800.cg have rank \(0\).
Complex multiplication
The elliptic curves in class 154800.cg do not have complex multiplication.Modular form 154800.2.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.
