Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 129792m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129792.m2 | 129792m1 | \([0, 1, 0, -563, 21945]\) | \(-8000/81\) | \(-200177422848\) | \([2]\) | \(138240\) | \(0.85076\) | \(\Gamma_0(N)\)-optimal |
129792.m1 | 129792m2 | \([0, 1, 0, -15773, 755067]\) | \(2744000/9\) | \(1423483895808\) | \([2]\) | \(276480\) | \(1.1973\) |
Rank
sage: E.rank()
The elliptic curves in class 129792m have rank \(1\).
Complex multiplication
The elliptic curves in class 129792m do not have complex multiplication.Modular form 129792.2.a.m
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 Cremona 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 Cremona labels.