Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 43758.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43758.f1 | 43758b2 | \([1, -1, 0, -105589752, -988471495360]\) | \(-6614510824496145219145875/17618041962927377281024\) | \(-346775919956299567022395392\) | \([]\) | \(13996800\) | \(3.7801\) | |
43758.f2 | 43758b1 | \([1, -1, 0, 11367543, 30665783709]\) | \(6016719201015220250419125/18530931219677304938224\) | \(-500335142931287233332048\) | \([3]\) | \(4665600\) | \(3.2308\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43758.f have rank \(0\).
Complex multiplication
The elliptic curves in class 43758.f do not have complex multiplication.Modular form 43758.2.a.f
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.