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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 11760y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11760.bk5 | 11760y1 | \([0, 1, 0, -751, 32360]\) | \(-24918016/229635\) | \(-432261249840\) | \([2]\) | \(12288\) | \(0.91514\) | \(\Gamma_0(N)\)-optimal |
| 11760.bk4 | 11760y2 | \([0, 1, 0, -20596, 1127804]\) | \(32082281296/99225\) | \(2988472838400\) | \([2, 2]\) | \(24576\) | \(1.2617\) | |
| 11760.bk3 | 11760y3 | \([0, 1, 0, -29416, 58820]\) | \(23366901604/13505625\) | \(1627057434240000\) | \([2, 2]\) | \(49152\) | \(1.6083\) | |
| 11760.bk1 | 11760y4 | \([0, 1, 0, -329296, 72622724]\) | \(32779037733124/315\) | \(37948861440\) | \([2]\) | \(49152\) | \(1.6083\) | |
| 11760.bk2 | 11760y5 | \([0, 1, 0, -317536, -68744236]\) | \(14695548366242/57421875\) | \(13835522400000000\) | \([2]\) | \(98304\) | \(1.9549\) | |
| 11760.bk6 | 11760y6 | \([0, 1, 0, 117584, 588020]\) | \(746185003198/432360075\) | \(-104175063989606400\) | \([2]\) | \(98304\) | \(1.9549\) |
Rank
sage: E.rank()
The elliptic curves in class 11760y have rank \(1\).
Complex multiplication
The elliptic curves in class 11760y do not have complex multiplication.Modular form 11760.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
