Properties

Label 6272.b
Number of curves $2$
Conductor $6272$
CM no
Rank $1$
Graph

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

Elliptic curves in class 6272.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6272.b1 6272g2 \([0, 1, 0, -457, 3303]\) \(10976\) \(963780608\) \([2]\) \(2304\) \(0.46310\)  
6272.b2 6272g1 \([0, 1, 0, 33, 265]\) \(128\) \(-30118144\) \([2]\) \(1152\) \(0.11653\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6272.b have rank \(1\).

Complex multiplication

The elliptic curves in class 6272.b do not have complex multiplication.

Modular form 6272.2.a.b

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