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Properties

Label 71478s
Number of curves $2$
Conductor $71478$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 71478s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
71478.bh1 71478s1 \([1, -1, 0, -4166910, 3274200468]\) \(233301213501481/63562752\) \(2179976570969269248\) \([2]\) \(2764800\) \(2.5017\) \(\Gamma_0(N)\)-optimal
71478.bh2 71478s2 \([1, -1, 0, -3647070, 4121019828]\) \(-156425280396841/123297834528\) \(-4228677677805482813472\) \([2]\) \(5529600\) \(2.8482\)  

Rank

sage: E.rank()
 

The elliptic curves in class 71478s have rank \(1\).

Complex multiplication

The elliptic curves in class 71478s do not have complex multiplication.

Modular form 71478.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 4 q^{5} - q^{8} - 4 q^{10} - q^{11} - 4 q^{13} + q^{16} + 2 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.