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Properties

Label 127050a
Number of curves $2$
Conductor $127050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 127050a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127050.o2 127050a1 \([1, 1, 0, -8041750, 7403276500]\) \(2765523913831303451/460886630400000\) \(9585001641600000000000\) \([2]\) \(8847360\) \(2.9391\) \(\Gamma_0(N)\)-optimal
127050.o1 127050a2 \([1, 1, 0, -36553750, -78047187500]\) \(259729608562018982171/23823922500000000\) \(495463138242187500000000\) \([2]\) \(17694720\) \(3.2857\)  

Rank

sage: E.rank()
 

The elliptic curves in class 127050a have rank \(1\).

Complex multiplication

The elliptic curves in class 127050a do not have complex multiplication.

Modular form 127050.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} - q^{12} + q^{14} + q^{16} + 4 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.