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SageMath
E = EllipticCurve("ek1")
E.isogeny_class()
Elliptic curves in class 296208.ek
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296208.ek1 | 296208ek2 | \([0, 0, 0, -21370899, 21959037650]\) | \(204055591784617/78708537864\) | \(416356579484383961972736\) | \([2]\) | \(30965760\) | \(3.2312\) | |
| 296208.ek2 | 296208ek1 | \([0, 0, 0, -9522579, -11066969518]\) | \(18052771191337/444958272\) | \(2353763761477998870528\) | \([2]\) | \(15482880\) | \(2.8846\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 296208.ek have rank \(2\).
Complex multiplication
The elliptic curves in class 296208.ek do not have complex multiplication.Modular form 296208.2.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.
