Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 94864.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
94864.t1 | 94864dc2 | \([0, 1, 0, -4934904, -4335698732]\) | \(-128667913/4096\) | \(-423106422088457519104\) | \([]\) | \(4561920\) | \(2.7338\) | |
94864.t2 | 94864dc1 | \([0, 1, 0, 282616, -21853196]\) | \(24167/16\) | \(-1652759461283037184\) | \([]\) | \(1520640\) | \(2.1845\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 94864.t have rank \(0\).
Complex multiplication
The elliptic curves in class 94864.t do not have complex multiplication.Modular form 94864.2.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.