Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 112360.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 112360.c1 | 112360c4 | \([0, 0, 0, -300563, -63421602]\) | \(132304644/5\) | \(113481528980480\) | \([2]\) | \(599040\) | \(1.7829\) | |
| 112360.c2 | 112360c2 | \([0, 0, 0, -19663, -893262]\) | \(148176/25\) | \(141851911225600\) | \([2, 2]\) | \(299520\) | \(1.4364\) | |
| 112360.c3 | 112360c1 | \([0, 0, 0, -5618, 148877]\) | \(55296/5\) | \(1773148890320\) | \([2]\) | \(149760\) | \(1.0898\) | \(\Gamma_0(N)\)-optimal |
| 112360.c4 | 112360c3 | \([0, 0, 0, 36517, -5061818]\) | \(237276/625\) | \(-14185191122560000\) | \([2]\) | \(599040\) | \(1.7829\) |
Rank
sage: E.rank()
The elliptic curves in class 112360.c have rank \(0\).
Complex multiplication
The elliptic curves in class 112360.c do not have complex multiplication.Modular form 112360.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
