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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 11760q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11760.u3 | 11760q1 | \([0, -1, 0, -15500, -737568]\) | \(13674725584/945\) | \(28461646080\) | \([2]\) | \(18432\) | \(1.0597\) | \(\Gamma_0(N)\)-optimal |
| 11760.u2 | 11760q2 | \([0, -1, 0, -16480, -638000]\) | \(4108974916/893025\) | \(107585022182400\) | \([2, 2]\) | \(36864\) | \(1.4063\) | |
| 11760.u1 | 11760q3 | \([0, -1, 0, -85080, 9020880]\) | \(282678688658/18600435\) | \(4481684638341120\) | \([2]\) | \(73728\) | \(1.7529\) | |
| 11760.u4 | 11760q4 | \([0, -1, 0, 36440, -3940208]\) | \(22208984782/40516875\) | \(-9762344605440000\) | \([2]\) | \(73728\) | \(1.7529\) |
Rank
sage: E.rank()
The elliptic curves in class 11760q have rank \(1\).
Complex multiplication
The elliptic curves in class 11760q do not have complex multiplication.Modular form 11760.2.a.q
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.
