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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 14490.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.p1 | 14490r4 | \([1, -1, 0, -4341240, 3408348456]\) | \(12411881707829361287041/303132494474220600\) | \(220983588471706817400\) | \([6]\) | \(995328\) | \(2.6878\) | |
| 14490.p2 | 14490r2 | \([1, -1, 0, -534240, -148345344]\) | \(23131609187144855041/322060536000000\) | \(234782130744000000\) | \([2]\) | \(331776\) | \(2.1385\) | |
| 14490.p3 | 14490r1 | \([1, -1, 0, -4320, -6220800]\) | \(-12232183057921/22933241856000\) | \(-16718333313024000\) | \([2]\) | \(165888\) | \(1.7919\) | \(\Gamma_0(N)\)-optimal |
| 14490.p4 | 14490r3 | \([1, -1, 0, 38880, 167935680]\) | \(8915971454369279/16719623332762560\) | \(-12188605409583906240\) | \([6]\) | \(497664\) | \(2.3412\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.p have rank \(0\).
Complex multiplication
The elliptic curves in class 14490.p do not have complex multiplication.Modular form 14490.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
