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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 40656i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40656.bi3 | 40656i1 | \([0, -1, 0, -887, -9810]\) | \(2725888/21\) | \(595244496\) | \([2]\) | \(23040\) | \(0.51276\) | \(\Gamma_0(N)\)-optimal |
40656.bi2 | 40656i2 | \([0, -1, 0, -1492, 5920]\) | \(810448/441\) | \(200002150656\) | \([2, 2]\) | \(46080\) | \(0.85933\) | |
40656.bi4 | 40656i3 | \([0, -1, 0, 5768, 40768]\) | \(11696828/7203\) | \(-13066807176192\) | \([2]\) | \(92160\) | \(1.2059\) | |
40656.bi1 | 40656i4 | \([0, -1, 0, -18432, 968112]\) | \(381775972/567\) | \(1028582489088\) | \([2]\) | \(92160\) | \(1.2059\) |
Rank
sage: E.rank()
The elliptic curves in class 40656i have rank \(0\).
Complex multiplication
The elliptic curves in class 40656i do not have complex multiplication.Modular form 40656.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.