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Properties

Label 271950.ba
Number of curves $2$
Conductor $271950$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 271950.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271950.ba1 271950ba2 \([1, 1, 0, -18575, 859125]\) \(132261232375/15968016\) \(85578585750000\) \([2]\) \(1327104\) \(1.4040\)  
271950.ba2 271950ba1 \([1, 1, 0, -4575, -106875]\) \(1976656375/255744\) \(1370628000000\) \([2]\) \(663552\) \(1.0574\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 271950.ba have rank \(2\).

Complex multiplication

The elliptic curves in class 271950.ba do not have complex multiplication.

Modular form 271950.2.a.ba

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