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Properties

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

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 50025.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50025.d1 50025n2 \([1, 0, 0, -2811313, -1814502508]\) \(157264717208387436361/4368589453125\) \(68259210205078125\) \([2]\) \(1585152\) \(2.3329\)  
50025.d2 50025n1 \([1, 0, 0, -168688, -30730633]\) \(-33974761330806841/6424789539375\) \(-100387336552734375\) \([2]\) \(792576\) \(1.9864\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 50025.2.a.d

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