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Properties

Label 215950.o
Number of curves $2$
Conductor $215950$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 215950.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215950.o1 215950bb2 \([1, -1, 0, -31769542, -301546607134]\) \(-226953328047600468451761/2382836194386693393110\) \(-37231815537292084267343750\) \([]\) \(146595456\) \(3.5887\)  
215950.o2 215950bb1 \([1, -1, 0, -3445792, 2499871616]\) \(-289581579184798874961/5081260310000000\) \(-79394692343750000000\) \([]\) \(20942208\) \(2.6158\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 215950.o have rank \(1\).

Complex multiplication

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

Modular form 215950.2.a.o

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.