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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 344850.eq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 344850.eq1 | 344850eq4 | \([1, 1, 1, -159790921188, 24585275999872281]\) | \(16300610738133468173382620881/2228489100\) | \(61686005913829687500\) | \([2]\) | \(806400000\) | \(4.6125\) | |
| 344850.eq2 | 344850eq3 | \([1, 1, 1, -9986931688, 384141888168281]\) | \(-3979640234041473454886161/1471455901872240\) | \(-40730842015260740103750000\) | \([2]\) | \(403200000\) | \(4.2659\) | |
| 344850.eq3 | 344850eq2 | \([1, 1, 1, -266033688, 1438807672281]\) | \(75224183150104868881/11219310000000000\) | \(310557688170468750000000000\) | \([2]\) | \(161280000\) | \(3.8078\) | |
| 344850.eq4 | 344850eq1 | \([1, 1, 1, 28238312, 122823288281]\) | \(89962967236397039/287450726400000\) | \(-7956820254873600000000000\) | \([2]\) | \(80640000\) | \(3.4612\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 344850.eq have rank \(0\).
Complex multiplication
The elliptic curves in class 344850.eq do not have complex multiplication.Modular form 344850.2.a.eq
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
