Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 207368.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
207368.g1 | 207368q2 | \([0, 1, 0, -12658088, 17328498592]\) | \(12576878500/1127\) | \(20099216529091632128\) | \([2]\) | \(8110080\) | \(2.7439\) | |
207368.g2 | 207368q1 | \([0, 1, 0, -734428, 311051040]\) | \(-9826000/3703\) | \(-16510070720325269248\) | \([2]\) | \(4055040\) | \(2.3974\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 207368.g have rank \(1\).
Complex multiplication
The elliptic curves in class 207368.g do not have complex multiplication.Modular form 207368.2.a.g
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.