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Properties

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

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 215950.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215950.bc1 215950j2 \([1, 1, 1, -84013, 8386531]\) \(4197043674447625/467985555968\) \(7312274312000000\) \([2]\) \(1741824\) \(1.7771\)  
215950.bc2 215950j1 \([1, 1, 1, -20013, -957469]\) \(56733768015625/7925399552\) \(123834368000000\) \([2]\) \(870912\) \(1.4305\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 215950.2.a.bc

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