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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 7616.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7616.k1 | 7616l2 | \([0, -1, 0, -1153, -12831]\) | \(5177717000/693889\) | \(22737354752\) | \([2]\) | \(7168\) | \(0.71480\) | |
| 7616.k2 | 7616l1 | \([0, -1, 0, -1113, -13927]\) | \(37259704000/833\) | \(3411968\) | \([2]\) | \(3584\) | \(0.36823\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7616.k have rank \(1\).
Complex multiplication
The elliptic curves in class 7616.k do not have complex multiplication.Modular form 7616.2.a.k
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.
