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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 37030.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37030.q1 | 37030o4 | \([1, -1, 1, -4542358, 3727369451]\) | \(70016546394529281/1610\) | \(238337781290\) | \([2]\) | \(540672\) | \(2.1576\) | |
| 37030.q2 | 37030o2 | \([1, -1, 1, -283908, 58288931]\) | \(17095749786081/2592100\) | \(383723827876900\) | \([2, 2]\) | \(270336\) | \(1.8111\) | |
| 37030.q3 | 37030o3 | \([1, -1, 1, -257458, 69567211]\) | \(-12748946194881/6718982410\) | \(-994650534239712490\) | \([2]\) | \(540672\) | \(2.1576\) | |
| 37030.q4 | 37030o1 | \([1, -1, 1, -19408, 733731]\) | \(5461074081/1610000\) | \(238337781290000\) | \([2]\) | \(135168\) | \(1.4645\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37030.q have rank \(0\).
Complex multiplication
The elliptic curves in class 37030.q do not have complex multiplication.Modular form 37030.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
