↑

Properties

Label 90774c
Number of curves $3$
Conductor $90774$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 90774c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90774.p2 90774c1 \([1, -1, 0, -5358, 154258]\) \(-132651/2\) \(-256505629014\) \([]\) \(138240\) \(0.99228\) \(\Gamma_0(N)\)-optimal
90774.p3 90774c2 \([1, -1, 0, 19857, 751013]\) \(9261/8\) \(-747970414204824\) \([]\) \(414720\) \(1.5416\)  
90774.p1 90774c3 \([1, -1, 0, -207078, -48040012]\) \(-1167051/512\) \(-430830958581978624\) \([]\) \(1244160\) \(2.0909\)  

Rank

sage: E.rank()
 

The elliptic curves in class 90774c have rank \(1\).

Complex multiplication

The elliptic curves in class 90774c do not have complex multiplication.

Modular form 90774.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} + q^{7} - q^{8} - 3 q^{10} + 3 q^{11} + 4 q^{13} - q^{14} + q^{16} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.