Properties

Label 43350.c
Number of curves $2$
Conductor $43350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 43350.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43350.c1 43350w2 \([1, 1, 0, -52403075, 145988392125]\) \(337575153545189/2448\) \(115407751781250000\) \([2]\) \(3686400\) \(2.8702\)  
43350.c2 43350w1 \([1, 1, 0, -3273075, 2283142125]\) \(-82256120549/221952\) \(-10463636161500000000\) \([2]\) \(1843200\) \(2.5236\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 43350.c have rank \(0\).

Complex multiplication

The elliptic curves in class 43350.c do not have complex multiplication.

Modular form 43350.2.a.c

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.