Properties

Label 29575i
Number of curves $3$
Conductor $29575$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 29575i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29575.o2 29575i1 \([0, -1, 1, -30983, 2113243]\) \(-43614208/91\) \(-6863119046875\) \([]\) \(72576\) \(1.3487\) \(\Gamma_0(N)\)-optimal
29575.o3 29575i2 \([0, -1, 1, 53517, 10415368]\) \(224755712/753571\) \(-56833488827171875\) \([]\) \(217728\) \(1.8980\)  
29575.o1 29575i3 \([0, -1, 1, -495733, -330943507]\) \(-178643795968/524596891\) \(-39564515544544046875\) \([]\) \(653184\) \(2.4473\)  

Rank

sage: E.rank()
 

The elliptic curves in class 29575i have rank \(0\).

Complex multiplication

The elliptic curves in class 29575i do not have complex multiplication.

Modular form 29575.2.a.i

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.