Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 26640.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26640.bb1 | 26640y2 | \([0, 0, 0, -58982067, -174352466574]\) | \(281470209323873024547/35046400\) | \(2825495720755200\) | \([2]\) | \(2027520\) | \(2.8262\) | |
26640.bb2 | 26640y1 | \([0, 0, 0, -3686067, -2724741774]\) | \(-68700855708416547/24248320000\) | \(-1954937579765760000\) | \([2]\) | \(1013760\) | \(2.4797\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26640.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 26640.bb do not have complex multiplication.Modular form 26640.2.a.bb
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.