Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 31680j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31680.l1 | 31680j1 | \([0, 0, 0, -1368, 18792]\) | \(379275264/15125\) | \(11290752000\) | \([2]\) | \(24576\) | \(0.69545\) | \(\Gamma_0(N)\)-optimal |
| 31680.l2 | 31680j2 | \([0, 0, 0, 612, 68688]\) | \(2122416/171875\) | \(-2052864000000\) | \([2]\) | \(49152\) | \(1.0420\) |
Rank
sage: E.rank()
The elliptic curves in class 31680j have rank \(0\).
Complex multiplication
The elliptic curves in class 31680j do not have complex multiplication.Modular form 31680.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
