Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 88935.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88935.p1 88935bd1 \([1, 1, 1, -80165, -5340070]\) \(205379/75\) \(20805764092384425\) \([2]\) \(760320\) \(1.8315\) \(\Gamma_0(N)\)-optimal
88935.p2 88935bd2 \([1, 1, 1, 245930, -37427818]\) \(5929741/5625\) \(-1560432306928831875\) \([2]\) \(1520640\) \(2.1781\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 88935.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} + 3 q^{8} + q^{9} - q^{10} + q^{12} - 4 q^{13} - q^{15} - q^{16} + 6 q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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.