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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 443760.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443760.i1 | 443760i2 | \([0, -1, 0, -15014496, -22382158080]\) | \(14457238157881/4437600\) | \(114899684008928870400\) | \([2]\) | \(21288960\) | \(2.8261\) | \(\Gamma_0(N)\)-optimal* |
443760.i2 | 443760i1 | \([0, -1, 0, -814176, -445503744]\) | \(-2305199161/1981440\) | \(-51304044952824053760\) | \([2]\) | \(10644480\) | \(2.4795\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 443760.i have rank \(1\).
Complex multiplication
The elliptic curves in class 443760.i do not have complex multiplication.Modular form 443760.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.