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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 40362u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40362.u2 | 40362u1 | \([1, 0, 1, -129, 484]\) | \(7880599/1008\) | \(30029328\) | \([2]\) | \(18432\) | \(0.16372\) | \(\Gamma_0(N)\)-optimal |
40362.u1 | 40362u2 | \([1, 0, 1, -1989, 33964]\) | \(29189662039/588\) | \(17517108\) | \([2]\) | \(36864\) | \(0.51029\) |
Rank
sage: E.rank()
The elliptic curves in class 40362u have rank \(0\).
Complex multiplication
The elliptic curves in class 40362u do not have complex multiplication.Modular form 40362.2.a.u
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.