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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 262080eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 262080.eb4 | 262080eb1 | \([0, 0, 0, 1572, -286288]\) | \(35969456/2985255\) | \(-35655694663680\) | \([2]\) | \(655360\) | \(1.2799\) | \(\Gamma_0(N)\)-optimal |
| 262080.eb3 | 262080eb2 | \([0, 0, 0, -56748, -5021872]\) | \(423026849956/16769025\) | \(801152645529600\) | \([2, 2]\) | \(1310720\) | \(1.6265\) | |
| 262080.eb2 | 262080eb3 | \([0, 0, 0, -147468, 15045392]\) | \(3711757787138/1124589375\) | \(107456188170240000\) | \([2]\) | \(2621440\) | \(1.9731\) | |
| 262080.eb1 | 262080eb4 | \([0, 0, 0, -899148, -328166512]\) | \(841356017734178/1404585\) | \(134210186772480\) | \([2]\) | \(2621440\) | \(1.9731\) |
Rank
sage: E.rank()
The elliptic curves in class 262080eb have rank \(1\).
Complex multiplication
The elliptic curves in class 262080eb do not have complex multiplication.Modular form 262080.2.a.eb
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
