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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 10830y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10830.w4 | 10830y1 | \([1, 1, 1, 4505, 103325]\) | \(214921799/218880\) | \(-10297402433280\) | \([4]\) | \(46080\) | \(1.1838\) | \(\Gamma_0(N)\)-optimal |
10830.w3 | 10830y2 | \([1, 1, 1, -24375, 923517]\) | \(34043726521/11696400\) | \(550267442528400\) | \([2, 2]\) | \(92160\) | \(1.5303\) | |
10830.w2 | 10830y3 | \([1, 1, 1, -161555, -24372475]\) | \(9912050027641/311647500\) | \(14661731198947500\) | \([2]\) | \(184320\) | \(1.8769\) | |
10830.w1 | 10830y4 | \([1, 1, 1, -349275, 79289397]\) | \(100162392144121/23457780\) | \(1103591926404180\) | \([2]\) | \(184320\) | \(1.8769\) |
Rank
sage: E.rank()
The elliptic curves in class 10830y have rank \(0\).
Complex multiplication
The elliptic curves in class 10830y do not have complex multiplication.Modular form 10830.2.a.y
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.