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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 38962.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38962.u1 | 38962z2 | \([1, 0, 0, -325674, -71561126]\) | \(2156338561552057/59530394\) | \(105461724325034\) | \([2]\) | \(414720\) | \(1.7939\) | |
38962.u2 | 38962z1 | \([1, 0, 0, -19544, -1212452]\) | \(-466025146777/87820348\) | \(-155579103523228\) | \([2]\) | \(207360\) | \(1.4473\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38962.u have rank \(1\).
Complex multiplication
The elliptic curves in class 38962.u do not have complex multiplication.Modular form 38962.2.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.