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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 10626l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10626.m4 | 10626l1 | \([1, 1, 1, 14938, 9775523]\) | \(368637286278891167/41443067603976192\) | \(-41443067603976192\) | \([4]\) | \(92160\) | \(1.8680\) | \(\Gamma_0(N)\)-optimal |
| 10626.m3 | 10626l2 | \([1, 1, 1, -604582, 174815651]\) | \(24439335640029940889953/902916953746891776\) | \(902916953746891776\) | \([2, 2]\) | \(184320\) | \(2.2146\) | |
| 10626.m2 | 10626l3 | \([1, 1, 1, -1535622, -494788317]\) | \(400476194988122984445793/126270124548858769248\) | \(126270124548858769248\) | \([2]\) | \(368640\) | \(2.5611\) | |
| 10626.m1 | 10626l4 | \([1, 1, 1, -9585862, 11419378211]\) | \(97413070452067229637409633/140666577176907936\) | \(140666577176907936\) | \([2]\) | \(368640\) | \(2.5611\) |
Rank
sage: E.rank()
The elliptic curves in class 10626l have rank \(1\).
Complex multiplication
The elliptic curves in class 10626l do not have complex multiplication.Modular form 10626.2.a.l
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.
