Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 17325b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17325.m2 | 17325b1 | \([1, -1, 1, 210745, -19455378]\) | \(2453656100384133/1805439453125\) | \(-761669769287109375\) | \([2]\) | \(192000\) | \(2.1195\) | \(\Gamma_0(N)\)-optimal |
| 17325.m1 | 17325b2 | \([1, -1, 1, -961130, -164767878]\) | \(232747967939865867/106810953528125\) | \(45060871019677734375\) | \([2]\) | \(384000\) | \(2.4660\) |
Rank
sage: E.rank()
The elliptic curves in class 17325b have rank \(0\).
Complex multiplication
The elliptic curves in class 17325b do not have complex multiplication.Modular form 17325.2.a.b
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.
