Show commands:
SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 190440bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190440.bn2 | 190440bd1 | \([0, 0, 0, -152544027, 756230370406]\) | \(-3552342505518244/179863605135\) | \(-19876403068206611477437440\) | \([2]\) | \(44605440\) | \(3.6149\) | \(\Gamma_0(N)\)-optimal |
| 190440.bn1 | 190440bd2 | \([0, 0, 0, -2469627507, 47238315229294]\) | \(7536914291382802562/17961229575\) | \(3969726264135946896537600\) | \([2]\) | \(89210880\) | \(3.9615\) |
Rank
sage: E.rank()
The elliptic curves in class 190440bd have rank \(0\).
Complex multiplication
The elliptic curves in class 190440bd do not have complex multiplication.Modular form 190440.2.a.bd
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.
