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SageMath
E = EllipticCurve("hv1")
E.isogeny_class()
Elliptic curves in class 62400.hv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62400.hv1 | 62400hk4 | \([0, 1, 0, -22752033, 41750856063]\) | \(2543984126301795848/909361981125\) | \(465593334336000000000\) | \([4]\) | \(4718592\) | \(2.9351\) | |
| 62400.hv2 | 62400hk3 | \([0, 1, 0, -11752033, -15191643937]\) | \(350584567631475848/8259273550125\) | \(4228748057664000000000\) | \([2]\) | \(4718592\) | \(2.9351\) | |
| 62400.hv3 | 62400hk2 | \([0, 1, 0, -1627033, 451481063]\) | \(7442744143086784/2927948765625\) | \(187388721000000000000\) | \([2, 2]\) | \(2359296\) | \(2.5885\) | |
| 62400.hv4 | 62400hk1 | \([0, 1, 0, 326092, 51090438]\) | \(3834800837445824/3342041015625\) | \(-3342041015625000000\) | \([2]\) | \(1179648\) | \(2.2419\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62400.hv have rank \(0\).
Complex multiplication
The elliptic curves in class 62400.hv do not have complex multiplication.Modular form 62400.2.a.hv
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
