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SageMath
E = EllipticCurve("ef1")
E.isogeny_class()
Elliptic curves in class 365904.ef
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 365904.ef1 | 365904ef2 | \([0, 0, 0, -2056395, 1135031546]\) | \(-545407363875/14\) | \(-24685979738112\) | \([]\) | \(3732480\) | \(2.0860\) | |
| 365904.ef2 | 365904ef1 | \([0, 0, 0, -23595, 1786202]\) | \(-7414875/2744\) | \(-537605780963328\) | \([]\) | \(1244160\) | \(1.5367\) | \(\Gamma_0(N)\)-optimal |
| 365904.ef3 | 365904ef3 | \([0, 0, 0, 179685, -18040374]\) | \(4492125/3584\) | \(-511888475849490432\) | \([]\) | \(3732480\) | \(2.0860\) |
Rank
sage: E.rank()
The elliptic curves in class 365904.ef have rank \(1\).
Complex multiplication
The elliptic curves in class 365904.ef do not have complex multiplication.Modular form 365904.2.a.ef
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
