Show commands:
SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 44352.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44352.bd1 | 44352br2 | \([0, 0, 0, -29676, -1816400]\) | \(15124197817/1294139\) | \(247313814257664\) | \([2]\) | \(147456\) | \(1.5030\) | |
44352.bd2 | 44352br1 | \([0, 0, 0, 2004, -131024]\) | \(4657463/41503\) | \(-7931346812928\) | \([2]\) | \(73728\) | \(1.1564\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44352.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 44352.bd do not have complex multiplication.Modular form 44352.2.a.bd
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.