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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 188760.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 188760.l1 | 188760cr4 | \([0, -1, 0, -16506376, -25599269540]\) | \(274171855990660996/2540331726075\) | \(4608361075688604748800\) | \([2]\) | \(12288000\) | \(2.9784\) | |
| 188760.l2 | 188760cr2 | \([0, -1, 0, -1804876, 281251060]\) | \(1433738629147984/754683125625\) | \(342263601335129760000\) | \([2, 2]\) | \(6144000\) | \(2.6318\) | |
| 188760.l3 | 188760cr1 | \([0, -1, 0, -1426751, 655746060]\) | \(11331632459167744/13573828125\) | \(384749832431250000\) | \([2]\) | \(3072000\) | \(2.2852\) | \(\Gamma_0(N)\)-optimal |
| 188760.l4 | 188760cr3 | \([0, -1, 0, 6846624, 2188041660]\) | \(19565773220287004/12465254233575\) | \(-22612949253413233228800\) | \([2]\) | \(12288000\) | \(2.9784\) |
Rank
sage: E.rank()
The elliptic curves in class 188760.l have rank \(0\).
Complex multiplication
The elliptic curves in class 188760.l do not have complex multiplication.Modular form 188760.2.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 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.
