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Properties

Label 324870.o
Number of curves $2$
Conductor $324870$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 324870.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
324870.o1 324870o1 \([1, 1, 0, -1303278, 466803828]\) \(6066707624375887/1172634840000\) \(47320045487867880000\) \([2]\) \(12902400\) \(2.4923\) \(\Gamma_0(N)\)-optimal
324870.o2 324870o2 \([1, 1, 0, 2661802, 2757827052]\) \(51685454328807473/111265903125000\) \(-4489980527206321875000\) \([2]\) \(25804800\) \(2.8389\)  

Rank

sage: E.rank()
 

The elliptic curves in class 324870.o have rank \(1\).

Complex multiplication

The elliptic curves in class 324870.o do not have complex multiplication.

Modular form 324870.2.a.o

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