Properties

Label 35574.h
Number of curves $4$
Conductor $35574$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 35574.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35574.h1 35574j4 \([1, 1, 0, -83794680, -295252549038]\) \(312196988566716625/25367712678\) \(5287199053762660068342\) \([2]\) \(3317760\) \(3.2135\)  
35574.h2 35574j3 \([1, 1, 0, -4879690, -5271526784]\) \(-61653281712625/21875235228\) \(-4559288591226498575292\) \([2]\) \(1658880\) \(2.8669\)  
35574.h3 35574j2 \([1, 1, 0, -2152350, 608689404]\) \(5290763640625/2291573592\) \(477615222193739009688\) \([2]\) \(1105920\) \(2.6642\)  
35574.h4 35574j1 \([1, 1, 0, 456410, 70763092]\) \(50447927375/39517632\) \(-8236358916921229248\) \([2]\) \(552960\) \(2.3176\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 35574.2.a.h

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.