Properties

Label 366275s
Number of curves $2$
Conductor $366275$
CM no
Rank $0$
Graph

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

Elliptic curves in class 366275s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
366275.s1 366275s1 \([0, 1, 1, -53516983, -150708228681]\) \(-9221261135586623488/121324931\) \(-223027450112796875\) \([]\) \(17915904\) \(2.8872\) \(\Gamma_0(N)\)-optimal
366275.s2 366275s2 \([0, 1, 1, -50491233, -168497329556]\) \(-7743965038771437568/2189290237869371\) \(-4024496987423337949671875\) \([]\) \(53747712\) \(3.4365\)  

Rank

sage: E.rank()
 

The elliptic curves in class 366275s have rank \(0\).

Complex multiplication

The elliptic curves in class 366275s do not have complex multiplication.

Modular form 366275.2.a.s

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.