Properties

Label 71148.c
Number of curves $2$
Conductor $71148$
CM no
Rank $2$
Graph

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

Elliptic curves in class 71148.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
71148.c1 71148bg2 \([0, -1, 0, -2160132, 1222712856]\) \(-2527934627152/9\) \(-3968637716736\) \([]\) \(1088640\) \(2.0593\)  
71148.c2 71148bg1 \([0, -1, 0, -25692, 1813176]\) \(-4253392/729\) \(-321459655055616\) \([]\) \(362880\) \(1.5100\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 71148.c have rank \(2\).

Complex multiplication

The elliptic curves in class 71148.c do not have complex multiplication.

Modular form 71148.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} + q^{9} - 5 q^{13} + 3 q^{15} + 3 q^{17} + 4 q^{19} + O(q^{20})\) 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.