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Properties

Label 40425.u
Number of curves $2$
Conductor $40425$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 40425.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40425.u1 40425ci1 \([1, 0, 0, -4838, -129333]\) \(2336752783/12375\) \(66322265625\) \([2]\) \(46080\) \(0.92116\) \(\Gamma_0(N)\)-optimal
40425.u2 40425ci2 \([1, 0, 0, -2213, -268458]\) \(-223648543/5671875\) \(-30397705078125\) \([2]\) \(92160\) \(1.2677\)  

Rank

sage: E.rank()
 

The elliptic curves in class 40425.u have rank \(1\).

Complex multiplication

The elliptic curves in class 40425.u do not have complex multiplication.

Modular form 40425.2.a.u

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