Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 7600m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7600.c3 | 7600m1 | \([0, 1, 0, 267, 163]\) | \(32768/19\) | \(-1216000000\) | \([]\) | \(2592\) | \(0.43269\) | \(\Gamma_0(N)\)-optimal |
7600.c2 | 7600m2 | \([0, 1, 0, -3733, 92163]\) | \(-89915392/6859\) | \(-438976000000\) | \([]\) | \(7776\) | \(0.98200\) | |
7600.c1 | 7600m3 | \([0, 1, 0, -307733, 65604163]\) | \(-50357871050752/19\) | \(-1216000000\) | \([]\) | \(23328\) | \(1.5313\) |
Rank
sage: E.rank()
The elliptic curves in class 7600m have rank \(0\).
Complex multiplication
The elliptic curves in class 7600m do not have complex multiplication.Modular form 7600.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.