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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 435120.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435120.y1 | 435120y3 | \([0, -1, 0, -4680496, 3898143040]\) | \(23531588875176481/6398929110\) | \(3083581894092349440\) | \([2]\) | \(11796480\) | \(2.5306\) | \(\Gamma_0(N)\)-optimal* |
435120.y2 | 435120y4 | \([0, -1, 0, -2250096, -1266033600]\) | \(2614441086442081/74385450090\) | \(35845627157046927360\) | \([2]\) | \(11796480\) | \(2.5306\) | |
435120.y3 | 435120y2 | \([0, -1, 0, -329296, 44720320]\) | \(8194759433281/2958272100\) | \(1425562641583718400\) | \([2, 2]\) | \(5898240\) | \(2.1841\) | \(\Gamma_0(N)\)-optimal* |
435120.y4 | 435120y1 | \([0, -1, 0, 62704, 4893120]\) | \(56578878719/54390000\) | \(-26210013634560000\) | \([2]\) | \(2949120\) | \(1.8375\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435120.y have rank \(0\).
Complex multiplication
The elliptic curves in class 435120.y do not have complex multiplication.Modular form 435120.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.