Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 14700.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14700.b1 | 14700w2 | \([0, -1, 0, -2829668, 1832440632]\) | \(665567485783184/257298363\) | \(968668643474784000\) | \([2]\) | \(387072\) | \(2.4166\) | |
14700.b2 | 14700w1 | \([0, -1, 0, -150593, 37460382]\) | \(-1605176213504/1640558367\) | \(-386020102638366000\) | \([2]\) | \(193536\) | \(2.0700\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14700.b have rank \(0\).
Complex multiplication
The elliptic curves in class 14700.b do not have complex multiplication.Modular form 14700.2.a.b
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.