Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 92778.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92778.b1 | 92778a2 | \([1, 1, 0, -84429130, 298562557396]\) | \(6174666627902151625/1282563072\) | \(13825023526111730688\) | \([2]\) | \(8478720\) | \(3.0595\) | |
92778.b2 | 92778a1 | \([1, 1, 0, -5258570, 4697272788]\) | \(-1491899855559625/21733834752\) | \(-234273684716711313408\) | \([2]\) | \(4239360\) | \(2.7130\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92778.b have rank \(0\).
Complex multiplication
The elliptic curves in class 92778.b do not have complex multiplication.Modular form 92778.2.a.b
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.