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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 59248x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59248.u2 | 59248x1 | \([0, 0, 0, -69299, 32680562]\) | \(-60698457/725788\) | \(-440085183715459072\) | \([2]\) | \(608256\) | \(2.0673\) | \(\Gamma_0(N)\)-optimal |
59248.u1 | 59248x2 | \([0, 0, 0, -2016019, 1098315090]\) | \(1494447319737/5411854\) | \(3281504739443531776\) | \([2]\) | \(1216512\) | \(2.4139\) |
Rank
sage: E.rank()
The elliptic curves in class 59248x have rank \(0\).
Complex multiplication
The elliptic curves in class 59248x do not have complex multiplication.Modular form 59248.2.a.x
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.