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Properties

Label 470400.fq
Number of curves $2$
Conductor $470400$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("fq1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 470400.fq have rank \(1\).

Complex multiplication

The elliptic curves in class 470400.fq do not have complex multiplication.

Modular form 470400.2.a.fq

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + 4 q^{11} - 2 q^{13} + 4 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 470400.fq

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
470400.fq1 470400fq1 \([0, -1, 0, -89481758, -325542396738]\) \(336751085874643808/271318359375\) \(63840667324218750000000\) \([2]\) \(70778880\) \(3.3056\) \(\Gamma_0(N)\)-optimal
470400.fq2 470400fq2 \([0, -1, 0, -70341133, -468733412363]\) \(-1277978627383936/2412172153125\) \(-72650148260608800000000000\) \([2]\) \(141557760\) \(3.6521\)