Properties

Label 129600iy
Number of curves $2$
Conductor $129600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("iy1")
 
E.isogeny_class()
 

Elliptic curves in class 129600iy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129600.bn2 129600iy1 \([0, 0, 0, -2700, 1674000]\) \(-9/5\) \(-1209323520000000\) \([]\) \(442368\) \(1.5732\) \(\Gamma_0(N)\)-optimal
129600.bn1 129600iy2 \([0, 0, 0, -3242700, -2257254000]\) \(-15590912409/78125\) \(-18895680000000000000\) \([]\) \(3096576\) \(2.5461\)  

Rank

sage: E.rank()
 

The elliptic curves in class 129600iy have rank \(1\).

Complex multiplication

The elliptic curves in class 129600iy do not have complex multiplication.

Modular form 129600.2.a.iy

sage: E.q_eigenform(10)
 
\(q - 3 q^{7} + 2 q^{11} - 2 q^{13} + 4 q^{17} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.