Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 43120.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43120.bw1 | 43120w1 | \([0, 0, 0, -1862, -29841]\) | \(379275264/15125\) | \(28471058000\) | \([2]\) | \(34560\) | \(0.77253\) | \(\Gamma_0(N)\)-optimal |
43120.bw2 | 43120w2 | \([0, 0, 0, 833, -109074]\) | \(2122416/171875\) | \(-5176556000000\) | \([2]\) | \(69120\) | \(1.1191\) |
Rank
sage: E.rank()
The elliptic curves in class 43120.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 43120.bw do not have complex multiplication.Modular form 43120.2.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.