Properties

Label 323400.ir
Number of curves $2$
Conductor $323400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ir1")
 
E.isogeny_class()
 

Elliptic curves in class 323400.ir

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
323400.ir1 323400ir2 \([0, 1, 0, -7345508, 7660225488]\) \(93141032522704/136125\) \(64059880500000000\) \([2]\) \(6635520\) \(2.4949\)  
323400.ir2 323400ir1 \([0, 1, 0, -454883, 121881738]\) \(-353912203264/13921875\) \(-409473667968750000\) \([2]\) \(3317760\) \(2.1483\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 323400.ir have rank \(0\).

Complex multiplication

The elliptic curves in class 323400.ir do not have complex multiplication.

Modular form 323400.2.a.ir

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} + q^{11} + 4 q^{17} + 4 q^{19} + O(q^{20})\) 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.