Properties

Label 92400.i
Number of curves $2$
Conductor $92400$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.i1 92400ex2 \([0, -1, 0, -112208, 1902912]\) \(19530306557/11114334\) \(88914672000000000\) \([2]\) \(737280\) \(1.9421\)  
92400.i2 92400ex1 \([0, -1, 0, 27792, 222912]\) \(296740963/174636\) \(-1397088000000000\) \([2]\) \(368640\) \(1.5955\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 92400.i have rank \(1\).

Complex multiplication

The elliptic curves in class 92400.i do not have complex multiplication.

Modular form 92400.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - q^{11} - 2 q^{13} - 2 q^{17} + 6 q^{19} + O(q^{20})\)  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.