Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 129472.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129472.bw1 | 129472a1 | \([0, 0, 0, -14051180, 19151031216]\) | \(9869198625/614656\) | \(19107872719802212548608\) | \([2]\) | \(6684672\) | \(3.0268\) | \(\Gamma_0(N)\)-optimal |
129472.bw2 | 129472a2 | \([0, 0, 0, 11103380, 80216241072]\) | \(4869777375/92236816\) | \(-2867375150015319520575488\) | \([2]\) | \(13369344\) | \(3.3734\) |
Rank
sage: E.rank()
The elliptic curves in class 129472.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 129472.bw do not have complex multiplication.Modular form 129472.2.a.bw
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 LMFDB 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 LMFDB labels.