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Properties

Label 90354m
Number of curves $2$
Conductor $90354$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 90354m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90354.r2 90354m1 \([1, 1, 1, 841, 8363]\) \(1298596571/1299078\) \(-65802197934\) \([]\) \(100800\) \(0.76275\) \(\Gamma_0(N)\)-optimal
90354.r1 90354m2 \([1, 1, 1, -157334, 23955059]\) \(-8503279704467029/46382688\) \(-2349422295264\) \([]\) \(504000\) \(1.5675\)  

Rank

sage: E.rank()
 

The elliptic curves in class 90354m have rank \(1\).

Complex multiplication

The elliptic curves in class 90354m do not have complex multiplication.

Modular form 90354.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 3 q^{5} - q^{6} - 2 q^{7} + q^{8} + q^{9} + 3 q^{10} - q^{11} - q^{12} + 4 q^{13} - 2 q^{14} - 3 q^{15} + q^{16} - 3 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.