Properties

Label 207214.s
Number of curves $2$
Conductor $207214$
CM no
Rank $1$
Graph

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

Elliptic curves in class 207214.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
207214.s1 207214d2 \([1, 0, 0, -261552, 50914432]\) \(42060685455433/516618368\) \(24304766263342208\) \([2]\) \(2935296\) \(1.9544\)  
207214.s2 207214d1 \([1, 0, 0, -30512, -792320]\) \(66775173193/32915456\) \(1548536626036736\) \([2]\) \(1467648\) \(1.6078\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 207214.s have rank \(1\).

Complex multiplication

The elliptic curves in class 207214.s do not have complex multiplication.

Modular form 207214.2.a.s

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