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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 45968.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45968.u1 | 45968f1 | \([0, -1, 0, -732, -2848]\) | \(35152/17\) | \(21006272768\) | \([2]\) | \(36864\) | \(0.67427\) | \(\Gamma_0(N)\)-optimal |
45968.u2 | 45968f2 | \([0, -1, 0, 2648, -24480]\) | \(415292/289\) | \(-1428426548224\) | \([2]\) | \(73728\) | \(1.0208\) |
Rank
sage: E.rank()
The elliptic curves in class 45968.u have rank \(0\).
Complex multiplication
The elliptic curves in class 45968.u do not have complex multiplication.Modular form 45968.2.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 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.