Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 49725.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49725.t1 | 49725c2 | \([1, -1, 0, -49317, -3009034]\) | \(43132764843/12138425\) | \(3733134676171875\) | \([2]\) | \(294912\) | \(1.6950\) | |
49725.t2 | 49725c1 | \([1, -1, 0, 8058, -312409]\) | \(188132517/244205\) | \(-75104484609375\) | \([2]\) | \(147456\) | \(1.3484\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 49725.t have rank \(0\).
Complex multiplication
The elliptic curves in class 49725.t do not have complex multiplication.Modular form 49725.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.