Properties

Label 271440b
Number of curves $2$
Conductor $271440$
CM no
Rank $0$
Graph

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

Elliptic curves in class 271440b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271440.b1 271440b1 \([0, 0, 0, -274323, -53955502]\) \(764579942079121/21285239040\) \(63557383209615360\) \([2]\) \(2654208\) \(2.0035\) \(\Gamma_0(N)\)-optimal
271440.b2 271440b2 \([0, 0, 0, 59757, -176963758]\) \(7903193128559/4535269736400\) \(-13542242868574617600\) \([2]\) \(5308416\) \(2.3501\)  

Rank

sage: E.rank()
 

The elliptic curves in class 271440b have rank \(0\).

Complex multiplication

The elliptic curves in class 271440b do not have complex multiplication.

Modular form 271440.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4 q^{7} - 4 q^{11} - q^{13} - 4 q^{17} + O(q^{20})\) 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.