Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 96600.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96600.q1 | 96600bm2 | \([0, -1, 0, -19808, -770388]\) | \(26860713266/7394247\) | \(236615904000000\) | \([2]\) | \(327680\) | \(1.4657\) | |
96600.q2 | 96600bm1 | \([0, -1, 0, 3192, -80388]\) | \(224727548/299943\) | \(-4799088000000\) | \([2]\) | \(163840\) | \(1.1191\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96600.q have rank \(0\).
Complex multiplication
The elliptic curves in class 96600.q do not have complex multiplication.Modular form 96600.2.a.q
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.