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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 442225cl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
442225.cl2 | 442225cl1 | \([1, 0, 1, -2896, -65537]\) | \(-9317\) | \(-288156021125\) | \([]\) | \(314496\) | \(0.93725\) | \(\Gamma_0(N)\)-optimal* |
442225.cl1 | 442225cl2 | \([1, 0, 1, -75117971, 250583824663]\) | \(-162677523113838677\) | \(-288156021125\) | \([]\) | \(11636352\) | \(2.7427\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 442225cl have rank \(0\).
Complex multiplication
The elliptic curves in class 442225cl do not have complex multiplication.Modular form 442225.2.a.cl
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.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.