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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 58800.ep
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.ep1 | 58800hk2 | \([0, -1, 0, -70741708, -228913595588]\) | \(665567485783184/257298363\) | \(15135447554293500000000\) | \([2]\) | \(7741440\) | \(3.2213\) | |
| 58800.ep2 | 58800hk1 | \([0, -1, 0, -3764833, -4675018088]\) | \(-1605176213504/1640558367\) | \(-6031564103724468750000\) | \([2]\) | \(3870720\) | \(2.8748\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58800.ep have rank \(0\).
Complex multiplication
The elliptic curves in class 58800.ep do not have complex multiplication.Modular form 58800.2.a.ep
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.
