Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 39710m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39710.j2 | 39710m1 | \([1, 0, 1, 3602, 336256]\) | \(109902239/1100000\) | \(-51750469100000\) | \([]\) | \(135000\) | \(1.3126\) | \(\Gamma_0(N)\)-optimal |
39710.j1 | 39710m2 | \([1, 0, 1, -2144348, 1208444416]\) | \(-23178622194826561/1610510\) | \(-75767861809310\) | \([]\) | \(675000\) | \(2.1173\) |
Rank
sage: E.rank()
The elliptic curves in class 39710m have rank \(0\).
Complex multiplication
The elliptic curves in class 39710m do not have complex multiplication.Modular form 39710.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.