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Properties

Label 50025m
Number of curves $2$
Conductor $50025$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 50025m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50025.v2 50025m1 \([1, 0, 1, -1876, 48773]\) \(-46694890801/39169575\) \(-612024609375\) \([2]\) \(70656\) \(0.95944\) \(\Gamma_0(N)\)-optimal
50025.v1 50025m2 \([1, 0, 1, -34501, 2463023]\) \(290656902035521/86293125\) \(1348330078125\) \([2]\) \(141312\) \(1.3060\)  

Rank

sage: E.rank()
 

The elliptic curves in class 50025m have rank \(0\).

Complex multiplication

The elliptic curves in class 50025m do not have complex multiplication.

Modular form 50025.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{6} + 4 q^{7} - 3 q^{8} + q^{9} + 2 q^{11} - q^{12} - 2 q^{13} + 4 q^{14} - q^{16} - 4 q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) 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.