Show commands:
SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 486178.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
486178.bh1 | 486178bh2 | \([1, -1, 0, -56985472924, -5235921987301384]\) | \(98191033604529537629349729/10906239337336\) | \(2273104360507847280702904\) | \([]\) | \(1659571200\) | \(4.5426\) | |
486178.bh2 | 486178bh1 | \([1, -1, 0, -114742084, 435504143696]\) | \(801581275315909089/70810888830976\) | \(14758573986369604748836864\) | \([]\) | \(237081600\) | \(3.5697\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 486178.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 486178.bh do not have complex multiplication.Modular form 486178.2.a.bh
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.