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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 58800.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.j1 | 58800fa2 | \([0, -1, 0, -2764008, 1835974512]\) | \(-6329617441/279936\) | \(-103281621295104000000\) | \([]\) | \(1975680\) | \(2.6053\) | |
| 58800.j2 | 58800fa1 | \([0, -1, 0, -20008, -2505488]\) | \(-2401/6\) | \(-2213683584000000\) | \([]\) | \(282240\) | \(1.6323\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58800.j have rank \(0\).
Complex multiplication
The elliptic curves in class 58800.j do not have complex multiplication.Modular form 58800.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
