Properties

Label 45864b
Number of curves $2$
Conductor $45864$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 45864b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
45864.cd1 45864b1 \([0, 0, 0, -4263, 106330]\) \(10536048/91\) \(74000279808\) \([2]\) \(86016\) \(0.90999\) \(\Gamma_0(N)\)-optimal
45864.cd2 45864b2 \([0, 0, 0, -1323, 250390]\) \(-78732/8281\) \(-26936101850112\) \([2]\) \(172032\) \(1.2566\)  

Rank

sage: E.rank()
 

The elliptic curves in class 45864b have rank \(0\).

Complex multiplication

The elliptic curves in class 45864b do not have complex multiplication.

Modular form 45864.2.a.b

sage: E.q_eigenform(10)
 
\(q + 4 q^{5} + 4 q^{11} - q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.