Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 52800.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52800.c1 | 52800ep4 | \([0, -1, 0, -155633, 12889137]\) | \(1628514404944/664335375\) | \(170069856000000000\) | \([2]\) | \(663552\) | \(2.0039\) | |
| 52800.c2 | 52800ep2 | \([0, -1, 0, -71633, -7354863]\) | \(158792223184/16335\) | \(4181760000000\) | \([2]\) | \(221184\) | \(1.4546\) | |
| 52800.c3 | 52800ep1 | \([0, -1, 0, -4133, -132363]\) | \(-488095744/200475\) | \(-3207600000000\) | \([2]\) | \(110592\) | \(1.1080\) | \(\Gamma_0(N)\)-optimal |
| 52800.c4 | 52800ep3 | \([0, -1, 0, 31867, 1451637]\) | \(223673040896/187171875\) | \(-2994750000000000\) | \([2]\) | \(331776\) | \(1.6573\) |
Rank
sage: E.rank()
The elliptic curves in class 52800.c have rank \(0\).
Complex multiplication
The elliptic curves in class 52800.c do not have complex multiplication.Modular form 52800.2.a.c
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
