Show commands:
SageMath
E = EllipticCurve("ed1")
E.isogeny_class()
Elliptic curves in class 92400.ed
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.ed1 | 92400bv4 | \([0, 1, 0, -950808, 356534388]\) | \(2970658109581346/2139291\) | \(68457312000000\) | \([2]\) | \(1048576\) | \(1.9666\) | |
| 92400.ed2 | 92400bv3 | \([0, 1, 0, -136808, -11613612]\) | \(8849350367426/3314597517\) | \(106067120544000000\) | \([2]\) | \(1048576\) | \(1.9666\) | |
| 92400.ed3 | 92400bv2 | \([0, 1, 0, -59808, 5480388]\) | \(1478729816932/38900169\) | \(622402704000000\) | \([2, 2]\) | \(524288\) | \(1.6201\) | |
| 92400.ed4 | 92400bv1 | \([0, 1, 0, 692, 277388]\) | \(9148592/8301447\) | \(-33205788000000\) | \([2]\) | \(262144\) | \(1.2735\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.ed have rank \(2\).
Complex multiplication
The elliptic curves in class 92400.ed do not have complex multiplication.Modular form 92400.2.a.ed
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
