Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 344850c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 344850.c4 | 344850c1 | \([1, 1, 0, 37750, 2476500]\) | \(214921799/218880\) | \(-6058738620000000\) | \([2]\) | \(3932160\) | \(1.7152\) | \(\Gamma_0(N)\)-optimal |
| 344850.c3 | 344850c2 | \([1, 1, 0, -204250, 22562500]\) | \(34043726521/11696400\) | \(323763845006250000\) | \([2, 2]\) | \(7864320\) | \(2.0618\) | |
| 344850.c1 | 344850c3 | \([1, 1, 0, -2926750, 1925590000]\) | \(100162392144121/23457780\) | \(649326378040312500\) | \([2]\) | \(15728640\) | \(2.4084\) | |
| 344850.c2 | 344850c4 | \([1, 1, 0, -1353750, -590121000]\) | \(9912050027641/311647500\) | \(8626602449179687500\) | \([2]\) | \(15728640\) | \(2.4084\) |
Rank
sage: E.rank()
The elliptic curves in class 344850c have rank \(3\).
Complex multiplication
The elliptic curves in class 344850c do not have complex multiplication.Modular form 344850.2.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 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.
