Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 38025bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38025.w2 | 38025bj1 | \([1, -1, 1, -2255, -41128]\) | \(-658489/9\) | \(-17325140625\) | \([]\) | \(26880\) | \(0.77144\) | \(\Gamma_0(N)\)-optimal |
| 38025.w1 | 38025bj2 | \([1, -1, 1, -16880, 4697372]\) | \(-276301129/4782969\) | \(-9207290058890625\) | \([]\) | \(188160\) | \(1.7444\) |
Rank
sage: E.rank()
The elliptic curves in class 38025bj have rank \(0\).
Complex multiplication
The elliptic curves in class 38025bj do not have complex multiplication.Modular form 38025.2.a.bj
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
