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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 6930x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6930.w4 | 6930x1 | \([1, -1, 1, -8573, -406843]\) | \(-95575628340361/43812679680\) | \(-31939443486720\) | \([2]\) | \(24576\) | \(1.2977\) | \(\Gamma_0(N)\)-optimal |
| 6930.w3 | 6930x2 | \([1, -1, 1, -149693, -22252219]\) | \(508859562767519881/62240270400\) | \(45373157121600\) | \([2, 2]\) | \(49152\) | \(1.6443\) | |
| 6930.w1 | 6930x3 | \([1, -1, 1, -2395013, -1426026283]\) | \(2084105208962185000201/31185000\) | \(22733865000\) | \([2]\) | \(98304\) | \(1.9908\) | |
| 6930.w2 | 6930x4 | \([1, -1, 1, -162293, -18275659]\) | \(648474704552553481/176469171805080\) | \(128646026245903320\) | \([2]\) | \(98304\) | \(1.9908\) |
Rank
sage: E.rank()
The elliptic curves in class 6930x have rank \(0\).
Complex multiplication
The elliptic curves in class 6930x do not have complex multiplication.Modular form 6930.2.a.x
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.
