Show commands:
SageMath
E = EllipticCurve("tf1")
E.isogeny_class()
Elliptic curves in class 1270080.tf
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
1270080.tf1 | \([0, 0, 0, -31752, -2167074]\) | \(884736/5\) | \(20007520706880\) | \([]\) | \(3732480\) | \(1.3942\) |
1270080.tf2 | \([0, 0, 0, -2352, 41846]\) | \(2359296/125\) | \(76236552000\) | \([]\) | \(1244160\) | \(0.84489\) |
Rank
sage: E.rank()
The elliptic curves in class 1270080.tf have rank \(2\).
Complex multiplication
The elliptic curves in class 1270080.tf do not have complex multiplication.Modular form 1270080.2.a.tf
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.