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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 336600.ee
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 336600.ee1 | 336600ee1 | \([0, 0, 0, -294375, -61411750]\) | \(967473250000/1153977\) | \(3364996932000000\) | \([2]\) | \(2211840\) | \(1.8905\) | \(\Gamma_0(N)\)-optimal |
| 336600.ee2 | 336600ee2 | \([0, 0, 0, -217875, -94077250]\) | \(-98061470500/271048833\) | \(-3161513588112000000\) | \([2]\) | \(4423680\) | \(2.2371\) |
Rank
sage: E.rank()
The elliptic curves in class 336600.ee have rank \(1\).
Complex multiplication
The elliptic curves in class 336600.ee do not have complex multiplication.Modular form 336600.2.a.ee
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.
