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Properties

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

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 25270.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25270.r1 25270p2 \([1, -1, 1, -380923, -92287253]\) \(-46905074216911089/1146880000000\) \(-149462548480000000\) \([]\) \(296352\) \(2.0807\)  
25270.r2 25270p1 \([1, -1, 1, -1873, 104921]\) \(-5573207889/32941720\) \(-4292997892120\) \([]\) \(42336\) \(1.1078\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 25270.2.a.r

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 LMFDB 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 LMFDB labels.