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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 435344.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435344.i1 | 435344i2 | \([0, 1, 0, -265048, 35763924]\) | \(104154702625/32188247\) | \(636381267205419008\) | \([2]\) | \(5160960\) | \(2.1208\) | \(\Gamma_0(N)\)-optimal* |
435344.i2 | 435344i1 | \([0, 1, 0, 45912, 3797236]\) | \(541343375/625807\) | \(-12372585921998848\) | \([2]\) | \(2580480\) | \(1.7742\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435344.i have rank \(0\).
Complex multiplication
The elliptic curves in class 435344.i do not have complex multiplication.Modular form 435344.2.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.