Show commands:
SageMath
E = EllipticCurve("qe1")
E.isogeny_class()
Elliptic curves in class 176400.qe
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.qe1 | 176400gi2 | \([0, 0, 0, -43365, 3479735]\) | \(-262885120/343\) | \(-11767111801200\) | \([]\) | \(497664\) | \(1.4151\) | |
176400.qe2 | 176400gi1 | \([0, 0, 0, 735, 22295]\) | \(1280/7\) | \(-240145138800\) | \([]\) | \(165888\) | \(0.86578\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.qe have rank \(0\).
Complex multiplication
The elliptic curves in class 176400.qe do not have complex multiplication.Modular form 176400.2.a.qe
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.