Properties

Label 127449v
Number of curves $2$
Conductor $127449$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 127449v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127449.b2 127449v1 \([0, 0, 1, -297381, -67827650]\) \(-28672/3\) \(-304317292534477803\) \([]\) \(1741824\) \(2.0938\) \(\Gamma_0(N)\)-optimal
127449.b1 127449v2 \([0, 0, 1, -116275971, 482982999700]\) \(-1713910976512/1594323\) \(-161726686261815418104123\) \([]\) \(22643712\) \(3.3763\)  

Rank

sage: E.rank()
 

The elliptic curves in class 127449v have rank \(2\).

Complex multiplication

The elliptic curves in class 127449v do not have complex multiplication.

Modular form 127449.2.a.v

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} - 2 q^{5} + 4 q^{10} - 2 q^{11} + q^{13} - 4 q^{16} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.