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SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 46800.eg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.eg1 | 46800fj2 | \([0, 0, 0, -23115, -230150]\) | \(3659383421/2056392\) | \(767544201216000\) | \([2]\) | \(147456\) | \(1.5463\) | |
| 46800.eg2 | 46800fj1 | \([0, 0, 0, 5685, -28550]\) | \(54439939/32448\) | \(-12111151104000\) | \([2]\) | \(73728\) | \(1.1997\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.eg have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.eg do not have complex multiplication.Modular form 46800.2.a.eg
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
