Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 331240bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 331240.bb1 | 331240bb1 | \([0, 0, 0, -111983963, -456119947738]\) | \(267080942160036/1990625\) | \(1157544683360374400000\) | \([2]\) | \(36126720\) | \(3.2177\) | \(\Gamma_0(N)\)-optimal |
| 331240.bb2 | 331240bb2 | \([0, 0, 0, -109665283, -475911736482]\) | \(-125415986034978/11552734375\) | \(-13435786503290060000000000\) | \([2]\) | \(72253440\) | \(3.5643\) |
Rank
sage: E.rank()
The elliptic curves in class 331240bb have rank \(2\).
Complex multiplication
The elliptic curves in class 331240bb do not have complex multiplication.Modular form 331240.2.a.bb
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.
