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Properties

Label 157470.z
Number of curves $2$
Conductor $157470$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 157470.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
157470.z1 157470b1 \([1, 0, 0, -106997980, 425993584400]\) \(-135472282703069439152665897921/240743885045760000000\) \(-240743885045760000000\) \([7]\) \(21425152\) \(3.1694\) \(\Gamma_0(N)\)-optimal
157470.z2 157470b2 \([1, 0, 0, 716932820, -2529437472640]\) \(40752954391814893896906735593279/26347975509292698179843819760\) \(-26347975509292698179843819760\) \([]\) \(149976064\) \(4.1423\)  

Rank

sage: E.rank()
 

The elliptic curves in class 157470.z have rank \(1\).

Complex multiplication

The elliptic curves in class 157470.z do not have complex multiplication.

Modular form 157470.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} + 5 q^{11} + q^{12} + q^{14} + q^{15} + q^{16} - 3 q^{17} + q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.