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Properties

Label 25270d
Number of curves $2$
Conductor $25270$
CM no
Rank $1$
Graph

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

Elliptic curves in class 25270d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25270.g2 25270d1 \([1, -1, 0, -676040, -716274760]\) \(-5573207889/32941720\) \(-201967867965928357720\) \([]\) \(804384\) \(2.5800\) \(\Gamma_0(N)\)-optimal
25270.g1 25270d2 \([1, -1, 0, -137513090, 633685831956]\) \(-46905074216911089/1146880000000\) \(-7031597269746810880000000\) \([]\) \(5630688\) \(3.5530\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25270d have rank \(1\).

Complex multiplication

The elliptic curves in class 25270d do not have complex multiplication.

Modular form 25270.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} - 3 q^{9} + q^{10} - 2 q^{11} - 2 q^{13} - q^{14} + q^{16} + 7 q^{17} + 3 q^{18} + O(q^{20})\) 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.