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Properties

Label 25050b
Number of curves $2$
Conductor $25050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 25050b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25050.b2 25050b1 \([1, 1, 0, -37000, 11800000]\) \(-358531401121921/3652290000000\) \(-57067031250000000\) \([]\) \(225792\) \(1.8975\) \(\Gamma_0(N)\)-optimal
25050.b1 25050b2 \([1, 1, 0, -9513250, -11470501250]\) \(-6093832136609347161121/108676727597808690\) \(-1698073868715760781250\) \([]\) \(1580544\) \(2.8704\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25050b have rank \(0\).

Complex multiplication

The elliptic curves in class 25050b do not have complex multiplication.

Modular form 25050.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} - 2 q^{11} - q^{12} + q^{14} + q^{16} - 4 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.