Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 45968.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45968.b1 | 45968v1 | \([0, 1, 0, -160944, -24903020]\) | \(23320116793/2873\) | \(56800961564672\) | \([2]\) | \(258048\) | \(1.6626\) | \(\Gamma_0(N)\)-optimal |
45968.b2 | 45968v2 | \([0, 1, 0, -147424, -29245644]\) | \(-17923019113/8254129\) | \(-163189162575302656\) | \([2]\) | \(516096\) | \(2.0092\) |
Rank
sage: E.rank()
The elliptic curves in class 45968.b have rank \(1\).
Complex multiplication
The elliptic curves in class 45968.b do not have complex multiplication.Modular form 45968.2.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.