Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 4400.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4400.t1 | 4400r1 | \([0, 1, 0, -408, -8812]\) | \(-117649/440\) | \(-28160000000\) | \([]\) | \(2304\) | \(0.69076\) | \(\Gamma_0(N)\)-optimal |
4400.t2 | 4400r2 | \([0, 1, 0, 3592, 207188]\) | \(80062991/332750\) | \(-21296000000000\) | \([]\) | \(6912\) | \(1.2401\) |
Rank
sage: E.rank()
The elliptic curves in class 4400.t have rank \(1\).
Complex multiplication
The elliptic curves in class 4400.t do not have complex multiplication.Modular form 4400.2.a.t
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.