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Properties

Label 57434b
Number of curves $3$
Conductor $57434$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 57434b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57434.c3 57434b1 \([1, 0, 1, 1058, -21662]\) \(12167/26\) \(-280259598554\) \([]\) \(70380\) \(0.88085\) \(\Gamma_0(N)\)-optimal
57434.c2 57434b2 \([1, 0, 1, -9987, 764742]\) \(-10218313/17576\) \(-189455488622504\) \([]\) \(211140\) \(1.4302\)  
57434.c1 57434b3 \([1, 0, 1, -1015082, 393555868]\) \(-10730978619193/6656\) \(-71746457229824\) \([]\) \(633420\) \(1.9795\)  

Rank

sage: E.rank()
 

The elliptic curves in class 57434b have rank \(0\).

Complex multiplication

The elliptic curves in class 57434b do not have complex multiplication.

Modular form 57434.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 3 q^{5} - q^{6} - q^{7} - q^{8} - 2 q^{9} - 3 q^{10} - 6 q^{11} + q^{12} - q^{13} + q^{14} + 3 q^{15} + q^{16} - 3 q^{17} + 2 q^{18} - 2 q^{19} + O(q^{20})\) 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 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.