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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 138624u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
138624.y2 | 138624u1 | \([0, 1, 0, 602, 9854]\) | \(4000/9\) | \(-54196854912\) | \([2]\) | \(115200\) | \(0.74377\) | \(\Gamma_0(N)\)-optimal |
138624.y1 | 138624u2 | \([0, 1, 0, -4813, 104075]\) | \(16000/3\) | \(2312399142912\) | \([2]\) | \(230400\) | \(1.0903\) |
Rank
sage: E.rank()
The elliptic curves in class 138624u have rank \(1\).
Complex multiplication
The elliptic curves in class 138624u do not have complex multiplication.Modular form 138624.2.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.