Properties

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

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

Elliptic curves in class 88935bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88935.o2 88935bc1 \([1, 1, 1, -1074620, 409016180]\) \(876440017817099/44659644435\) \(6993290298325442265\) \([2]\) \(1935360\) \(2.3741\) \(\Gamma_0(N)\)-optimal
88935.o1 88935bc2 \([1, 1, 1, -3039275, -1515559858]\) \(19827475353801179/5148111413025\) \(806146982468832017475\) \([2]\) \(3870720\) \(2.7206\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 88935.2.a.bc

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