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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 62400.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62400.cl1 | 62400y4 | \([0, -1, 0, -581633, 170875137]\) | \(10625310339698/3855735\) | \(7896545280000000\) | \([4]\) | \(589824\) | \(2.0189\) | |
| 62400.cl2 | 62400y3 | \([0, -1, 0, -301633, -62364863]\) | \(1481943889298/34543665\) | \(70745425920000000\) | \([2]\) | \(589824\) | \(2.0189\) | |
| 62400.cl3 | 62400y2 | \([0, -1, 0, -41633, 1855137]\) | \(7793764996/3080025\) | \(3153945600000000\) | \([2, 2]\) | \(294912\) | \(1.6724\) | |
| 62400.cl4 | 62400y1 | \([0, -1, 0, 8367, 205137]\) | \(253012016/219375\) | \(-56160000000000\) | \([2]\) | \(147456\) | \(1.3258\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62400.cl have rank \(0\).
Complex multiplication
The elliptic curves in class 62400.cl do not have complex multiplication.Modular form 62400.2.a.cl
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.
