Properties

Label 10304y
Number of curves $2$
Conductor $10304$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10304y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10304.bb2 10304y1 \([0, -1, 0, 2207, -188415]\) \(4533086375/60669952\) \(-15904263897088\) \([2]\) \(21504\) \(1.2139\) \(\Gamma_0(N)\)-optimal
10304.bb1 10304y2 \([0, -1, 0, -38753, -2736127]\) \(24553362849625/1755162752\) \(460105384460288\) \([2]\) \(43008\) \(1.5605\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10304y have rank \(1\).

Complex multiplication

The elliptic curves in class 10304y do not have complex multiplication.

Modular form 10304.2.a.y

sage: E.q_eigenform(10)
 
\(q + 2q^{3} - q^{7} + q^{9} + 4q^{11} + 6q^{17} - 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.