Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1368.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1368.f1 | 1368b1 | \([0, 0, 0, -135, 378]\) | \(54000/19\) | \(95738112\) | \([2]\) | \(192\) | \(0.23271\) | \(\Gamma_0(N)\)-optimal |
1368.f2 | 1368b2 | \([0, 0, 0, 405, 2646]\) | \(364500/361\) | \(-7276096512\) | \([2]\) | \(384\) | \(0.57929\) |
Rank
sage: E.rank()
The elliptic curves in class 1368.f have rank \(0\).
Complex multiplication
The elliptic curves in class 1368.f do not have complex multiplication.Modular form 1368.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.