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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 377706.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377706.cl1 | 377706cl4 | \([1, 1, 1, -2686802, -1696243417]\) | \(14489843500598257/6246072\) | \(924642821278008\) | \([2]\) | \(8650752\) | \(2.2143\) | |
| 377706.cl2 | 377706cl3 | \([1, 1, 1, -359202, 43650279]\) | \(34623662831857/14438442312\) | \(2137407643432135368\) | \([2]\) | \(8650752\) | \(2.2143\) | |
| 377706.cl3 | 377706cl2 | \([1, 1, 1, -168762, -26279289]\) | \(3590714269297/73410624\) | \(10867406985884736\) | \([2, 2]\) | \(4325376\) | \(1.8677\) | |
| 377706.cl4 | 377706cl1 | \([1, 1, 1, 518, -1225849]\) | \(103823/4386816\) | \(-649406206439424\) | \([2]\) | \(2162688\) | \(1.5212\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 377706.cl have rank \(2\).
Complex multiplication
The elliptic curves in class 377706.cl do not have complex multiplication.Modular form 377706.2.a.cl
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.
