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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 285318u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
285318.u2 | 285318u1 | \([1, -1, 0, -43038, 3444282]\) | \(6826561273/7074\) | \(9135844412706\) | \([]\) | \(1641600\) | \(1.4047\) | \(\Gamma_0(N)\)-optimal |
285318.u1 | 285318u2 | \([1, -1, 0, -157383, -20362347]\) | \(333822098953/53954184\) | \(69680100429532296\) | \([]\) | \(4924800\) | \(1.9540\) |
Rank
sage: E.rank()
The elliptic curves in class 285318u have rank \(1\).
Complex multiplication
The elliptic curves in class 285318u do not have complex multiplication.Modular form 285318.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.