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SageMath
E = EllipticCurve("ek1")
E.isogeny_class()
Elliptic curves in class 55440ek
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55440.ee2 | 55440ek1 | \([0, 0, 0, -740892, -336961501]\) | \(-3856034557002072064/1973796785296875\) | \(-23022365703702750000\) | \([2]\) | \(1290240\) | \(2.4199\) | \(\Gamma_0(N)\)-optimal |
| 55440.ee1 | 55440ek2 | \([0, 0, 0, -13042767, -18127933126]\) | \(1314817350433665559504/190690249278375\) | \(35587377081327456000\) | \([2]\) | \(2580480\) | \(2.7665\) |
Rank
sage: E.rank()
The elliptic curves in class 55440ek have rank \(1\).
Complex multiplication
The elliptic curves in class 55440ek do not have complex multiplication.Modular form 55440.2.a.ek
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 Cremona 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 Cremona labels.
