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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 42320.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 42320.l1 | 42320c4 | \([0, 0, 0, -56603, -5183142]\) | \(132304644/5\) | \(757943751680\) | \([2]\) | \(98560\) | \(1.3655\) | |
| 42320.l2 | 42320c2 | \([0, 0, 0, -3703, -73002]\) | \(148176/25\) | \(947429689600\) | \([2, 2]\) | \(49280\) | \(1.0190\) | |
| 42320.l3 | 42320c1 | \([0, 0, 0, -1058, 12167]\) | \(55296/5\) | \(11842871120\) | \([2]\) | \(24640\) | \(0.67239\) | \(\Gamma_0(N)\)-optimal |
| 42320.l4 | 42320c3 | \([0, 0, 0, 6877, -413678]\) | \(237276/625\) | \(-94742968960000\) | \([2]\) | \(98560\) | \(1.3655\) |
Rank
sage: E.rank()
The elliptic curves in class 42320.l have rank \(0\).
Complex multiplication
The elliptic curves in class 42320.l do not have complex multiplication.Modular form 42320.2.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.
