Properties

Label 25350g
Number of curves $4$
Conductor $25350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 25350g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25350.v4 25350g1 \([1, 1, 0, -1219000, 855304000]\) \(-2656166199049/2658140160\) \(-200473981992960000000\) \([2]\) \(1290240\) \(2.5913\) \(\Gamma_0(N)\)-optimal
25350.v3 25350g2 \([1, 1, 0, -22851000, 42021000000]\) \(17496824387403529/6580454400\) \(496290570656400000000\) \([2, 2]\) \(2580480\) \(2.9379\)  
25350.v2 25350g3 \([1, 1, 0, -26231000, 28768020000]\) \(26465989780414729/10571870144160\) \(797318718104106022500000\) \([2]\) \(5160960\) \(3.2845\)  
25350.v1 25350g4 \([1, 1, 0, -365583000, 2690311164000]\) \(71647584155243142409/10140000\) \(764747550937500000\) \([2]\) \(5160960\) \(3.2845\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 25350.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + 4 q^{7} - q^{8} + q^{9} - q^{12} - 4 q^{14} + q^{16} + 2 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.