Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 38148.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38148.j1 | 38148n2 | \([0, 1, 0, -373484, 87726132]\) | \(932410994128/29403\) | \(181687536974592\) | \([2]\) | \(295680\) | \(1.8320\) | |
38148.j2 | 38148n1 | \([0, 1, 0, -22349, 1487376]\) | \(-3196715008/649539\) | \(-250852678891056\) | \([2]\) | \(147840\) | \(1.4854\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38148.j have rank \(0\).
Complex multiplication
The elliptic curves in class 38148.j do not have complex multiplication.Modular form 38148.2.a.j
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.