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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 3120q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3120.b3 | 3120q1 | \([0, -1, 0, -96, -2304]\) | \(-24137569/561600\) | \(-2300313600\) | \([2]\) | \(1152\) | \(0.47709\) | \(\Gamma_0(N)\)-optimal |
| 3120.b2 | 3120q2 | \([0, -1, 0, -3296, -71424]\) | \(967068262369/4928040\) | \(20185251840\) | \([2]\) | \(2304\) | \(0.82366\) | |
| 3120.b4 | 3120q3 | \([0, -1, 0, 864, 61440]\) | \(17394111071/411937500\) | \(-1687296000000\) | \([2]\) | \(3456\) | \(1.0264\) | |
| 3120.b1 | 3120q4 | \([0, -1, 0, -19136, 973440]\) | \(189208196468929/10860320250\) | \(44483871744000\) | \([2]\) | \(6912\) | \(1.3730\) |
Rank
sage: E.rank()
The elliptic curves in class 3120q have rank \(1\).
Complex multiplication
The elliptic curves in class 3120q do not have complex multiplication.Modular form 3120.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
