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Properties

Label 35574.g
Number of curves $2$
Conductor $35574$
CM no
Rank $1$
Graph

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

Elliptic curves in class 35574.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35574.g1 35574h2 \([1, 1, 0, -140725, 20260717]\) \(-29343015625/192\) \(-2016688352448\) \([]\) \(142560\) \(1.5444\)  
35574.g2 35574h1 \([1, 1, 0, -970, 52144]\) \(-9625/108\) \(-1134387198252\) \([]\) \(47520\) \(0.99508\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35574.g have rank \(1\).

Complex multiplication

The elliptic curves in class 35574.g do not have complex multiplication.

Modular form 35574.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - q^{12} + q^{13} + q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.