Properties

Label 49725c
Number of curves $2$
Conductor $49725$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 49725c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49725.t2 49725c1 \([1, -1, 0, 8058, -312409]\) \(188132517/244205\) \(-75104484609375\) \([2]\) \(147456\) \(1.3484\) \(\Gamma_0(N)\)-optimal
49725.t1 49725c2 \([1, -1, 0, -49317, -3009034]\) \(43132764843/12138425\) \(3733134676171875\) \([2]\) \(294912\) \(1.6950\)  

Rank

sage: E.rank()
 

The elliptic curves in class 49725c have rank \(0\).

Complex multiplication

The elliptic curves in class 49725c do not have complex multiplication.

Modular form 49725.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 4 q^{7} - 3 q^{8} + 2 q^{11} + q^{13} - 4 q^{14} - q^{16} - q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.