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Properties

Label 270725.m
Number of curves $2$
Conductor $270725$
CM no
Rank $1$
Graph

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

Elliptic curves in class 270725.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270725.m1 270725m1 \([1, 1, 1, -72913, -7607594]\) \(23320116793/2873\) \(5281337140625\) \([2]\) \(1105920\) \(1.4647\) \(\Gamma_0(N)\)-optimal
270725.m2 270725m2 \([1, 1, 1, -66788, -8930594]\) \(-17923019113/8254129\) \(-15173281605015625\) \([2]\) \(2211840\) \(1.8112\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270725.m have rank \(1\).

Complex multiplication

The elliptic curves in class 270725.m do not have complex multiplication.

Modular form 270725.2.a.m

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