Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 101150.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101150.g1 | 101150v2 | \([1, 0, 1, -859076, -306546702]\) | \(-24843904907425/5488\) | \(-15488593750000\) | \([]\) | \(1244160\) | \(1.9140\) | |
101150.g2 | 101150v1 | \([1, 0, 1, -9076, -546702]\) | \(-29291425/28672\) | \(-80920000000000\) | \([]\) | \(414720\) | \(1.3647\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101150.g have rank \(0\).
Complex multiplication
The elliptic curves in class 101150.g do not have complex multiplication.Modular form 101150.2.a.g
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.