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Properties

Label 25350f
Number of curves $2$
Conductor $25350$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 25350f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25350.f2 25350f1 \([1, 1, 0, -1058450, -379663500]\) \(16462225/1728\) \(13765455916875000000\) \([]\) \(898560\) \(2.4073\) \(\Gamma_0(N)\)-optimal
25350.f1 25350f2 \([1, 1, 0, -83445950, -293432001000]\) \(8066639494225/12\) \(95593443867187500\) \([]\) \(2695680\) \(2.9566\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25350f have rank \(1\).

Complex multiplication

The elliptic curves in class 25350f do not have complex multiplication.

Modular form 25350.2.a.f

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