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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 478350.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
478350.u1 | 478350u1 | \([1, -1, 1, -257486855, -1590330052353]\) | \(-165745346665991446425889/10662541623558144\) | \(-121453013180841984000000\) | \([]\) | \(110638080\) | \(3.4870\) | \(\Gamma_0(N)\)-optimal* |
478350.u2 | 478350u2 | \([1, -1, 1, 1770672145, 45706565761647]\) | \(53900230693869615719525471/110424476261224735356024\) | \(-1257803799913013001164710875000\) | \([]\) | \(774466560\) | \(4.4600\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 478350.u have rank \(0\).
Complex multiplication
The elliptic curves in class 478350.u do not have complex multiplication.Modular form 478350.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.