Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 3120u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3120.q3 | 3120u1 | \([0, 1, 0, -216, -1260]\) | \(273359449/9360\) | \(38338560\) | \([2]\) | \(768\) | \(0.22703\) | \(\Gamma_0(N)\)-optimal |
3120.q2 | 3120u2 | \([0, 1, 0, -536, 2964]\) | \(4165509529/1368900\) | \(5607014400\) | \([2, 2]\) | \(1536\) | \(0.57361\) | |
3120.q1 | 3120u3 | \([0, 1, 0, -7736, 259284]\) | \(12501706118329/2570490\) | \(10528727040\) | \([2]\) | \(3072\) | \(0.92018\) | |
3120.q4 | 3120u4 | \([0, 1, 0, 1544, 22100]\) | \(99317171591/106616250\) | \(-436700160000\) | \([2]\) | \(3072\) | \(0.92018\) |
Rank
sage: E.rank()
The elliptic curves in class 3120u have rank \(1\).
Complex multiplication
The elliptic curves in class 3120u do not have complex multiplication.Modular form 3120.2.a.u
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.