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SageMath
E = EllipticCurve("ek1")
E.isogeny_class()
Elliptic curves in class 262080.ek
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 262080.ek1 | 262080ek2 | \([0, 0, 0, -39569388, -95766048688]\) | \(1936101054887046531846/905403781953125\) | \(3204173281720320000000\) | \([2]\) | \(21331968\) | \(3.0826\) | |
| 262080.ek2 | 262080ek1 | \([0, 0, 0, -2069388, -2001048688]\) | \(-553867390580563692/657061767578125\) | \(-1162652400000000000000\) | \([2]\) | \(10665984\) | \(2.7360\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 262080.ek have rank \(0\).
Complex multiplication
The elliptic curves in class 262080.ek do not have complex multiplication.Modular form 262080.2.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 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.
