Properties

Label 88935.ba
Number of curves $2$
Conductor $88935$
CM no
Rank $1$
Graph

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

Elliptic curves in class 88935.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88935.ba1 88935k2 \([0, -1, 1, -21088041, -42595901503]\) \(-11947588428895092736/2118439154286675\) \(-183894265143755556234075\) \([]\) \(9331200\) \(3.1896\)  
88935.ba2 88935k1 \([0, -1, 1, 1780959, 260032772]\) \(7196694080651264/4502793796875\) \(-390871720197697921875\) \([]\) \(3110400\) \(2.6403\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 88935.ba have rank \(1\).

Complex multiplication

The elliptic curves in class 88935.ba do not have complex multiplication.

Modular form 88935.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} - q^{5} + q^{9} + 2 q^{12} - q^{13} + q^{15} + 4 q^{16} - 6 q^{17} - 7 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.