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Properties

Label 25270u
Number of curves $2$
Conductor $25270$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 25270u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25270.w1 25270u1 \([1, 1, 1, -1271, -86561]\) \(-4826809/65170\) \(-3065980064770\) \([]\) \(51840\) \(1.0776\) \(\Gamma_0(N)\)-optimal
25270.w2 25270u2 \([1, 1, 1, 11364, 2243333]\) \(3449795831/48013000\) \(-2258813884453000\) \([]\) \(155520\) \(1.6269\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25270u have rank \(0\).

Complex multiplication

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

Modular form 25270.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} - q^{5} + 2 q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - 3 q^{11} + 2 q^{12} - 5 q^{13} + q^{14} - 2 q^{15} + q^{16} - 3 q^{17} + q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.