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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 880.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
880.i1 | 880g2 | \([0, 1, 0, -95040, 11245748]\) | \(-23178622194826561/1610510\) | \(-6596648960\) | \([]\) | \(2400\) | \(1.3382\) | |
880.i2 | 880g1 | \([0, 1, 0, 160, 3188]\) | \(109902239/1100000\) | \(-4505600000\) | \([]\) | \(480\) | \(0.53350\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 880.i have rank \(1\).
Complex multiplication
The elliptic curves in class 880.i do not have complex multiplication.Modular form 880.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.