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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 143745k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
143745.f4 | 143745k1 | \([1, 1, 1, 56785, 3551372]\) | \(7892485271/6662775\) | \(-17094857774724975\) | \([4]\) | \(875520\) | \(1.8024\) | \(\Gamma_0(N)\)-optimal |
143745.f3 | 143745k2 | \([1, 1, 1, -278620, 30920420]\) | \(932288503609/377330625\) | \(968127149486975625\) | \([2, 2]\) | \(1751040\) | \(2.1490\) | |
143745.f1 | 143745k3 | \([1, 1, 1, -3872245, 2930257070]\) | \(2502660030961609/983934525\) | \(2524506795519370725\) | \([2]\) | \(3502080\) | \(2.4956\) | |
143745.f2 | 143745k4 | \([1, 1, 1, -2051475, -1110089058]\) | \(372144896498089/8194921875\) | \(21025927474379296875\) | \([2]\) | \(3502080\) | \(2.4956\) |
Rank
sage: E.rank()
The elliptic curves in class 143745k have rank \(1\).
Complex multiplication
The elliptic curves in class 143745k do not have complex multiplication.Modular form 143745.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.