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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 10830.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10830.i1 | 10830k2 | \([1, 0, 1, -26684, -1675654]\) | \(306331959547531/900000000\) | \(6173100000000\) | \([2]\) | \(61440\) | \(1.3244\) | |
10830.i2 | 10830k1 | \([1, 0, 1, -2364, -2438]\) | \(212883113611/122880000\) | \(842833920000\) | \([2]\) | \(30720\) | \(0.97786\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10830.i have rank \(0\).
Complex multiplication
The elliptic curves in class 10830.i do not have complex multiplication.Modular form 10830.2.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.