Show commands:
SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 15680.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15680.bk1 | 15680bh1 | \([0, -1, 0, -3985, 98225]\) | \(-177953104/125\) | \(-4917248000\) | \([]\) | \(13824\) | \(0.79596\) | \(\Gamma_0(N)\)-optimal |
15680.bk2 | 15680bh2 | \([0, -1, 0, 3855, 410257]\) | \(161017136/1953125\) | \(-76832000000000\) | \([]\) | \(41472\) | \(1.3453\) |
Rank
sage: E.rank()
The elliptic curves in class 15680.bk have rank \(2\).
Complex multiplication
The elliptic curves in class 15680.bk do not have complex multiplication.Modular form 15680.2.a.bk
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.