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Properties

Label 215950.r
Number of curves $2$
Conductor $215950$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 215950.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215950.r1 215950b2 \([1, 0, 0, -91788, 10695442]\) \(5473456901241337/261152654\) \(4080510218750\) \([2]\) \(933888\) \(1.4933\)  
215950.r2 215950b1 \([1, 0, 0, -6038, 148192]\) \(1558071944857/290357732\) \(4536839562500\) \([2]\) \(466944\) \(1.1467\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 215950.r have rank \(0\).

Complex multiplication

The elliptic curves in class 215950.r do not have complex multiplication.

Modular form 215950.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} - 2 q^{6} + q^{7} + q^{8} + q^{9} + 4 q^{11} - 2 q^{12} - 2 q^{13} + q^{14} + q^{16} + 4 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.