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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 54720.cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54720.cg1 | 54720cu2 | \([0, 0, 0, -34668, -2460592]\) | \(651038076963/7220000\) | \(51102351360000\) | \([2]\) | \(245760\) | \(1.4447\) | |
| 54720.cg2 | 54720cu1 | \([0, 0, 0, -3948, 33872]\) | \(961504803/486400\) | \(3442684723200\) | \([2]\) | \(122880\) | \(1.0982\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54720.cg have rank \(0\).
Complex multiplication
The elliptic curves in class 54720.cg do not have complex multiplication.Modular form 54720.2.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.
