Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 2142.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2142.j1 | 2142b1 | \([1, -1, 0, -168, 882]\) | \(-19486825371/11662\) | \(-314874\) | \([3]\) | \(480\) | \(-0.00098777\) | \(\Gamma_0(N)\)-optimal |
2142.j2 | 2142b2 | \([1, -1, 0, 147, 3437]\) | \(17779581/275128\) | \(-5415344424\) | \([]\) | \(1440\) | \(0.54832\) |
Rank
sage: E.rank()
The elliptic curves in class 2142.j have rank \(0\).
Complex multiplication
The elliptic curves in class 2142.j do not have complex multiplication.Modular form 2142.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.