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Properties

Label 29575w
Number of curves $2$
Conductor $29575$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 29575w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29575.f2 29575w1 \([0, 1, 1, 7042, -315506]\) \(4096/7\) \(-65991529296875\) \([]\) \(93600\) \(1.3367\) \(\Gamma_0(N)\)-optimal
29575.f1 29575w2 \([0, 1, 1, -626708, 191710744]\) \(-2887553024/16807\) \(-158445661841796875\) \([]\) \(468000\) \(2.1414\)  

Rank

sage: E.rank()
 

The elliptic curves in class 29575w have rank \(1\).

Complex multiplication

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

Modular form 29575.2.a.w

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{6} + q^{7} - 2 q^{9} + 3 q^{11} + 2 q^{12} - 2 q^{14} - 4 q^{16} + 7 q^{17} + 4 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.