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Properties

Label 478864.a
Number of curves $2$
Conductor $478864$
CM no
Rank $0$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 478864.a have rank \(0\).

Complex multiplication

The elliptic curves in class 478864.a do not have complex multiplication.

Modular form 478864.2.a.a

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{3} - 2 q^{5} - 2 q^{7} + q^{9} - 2 q^{11} + 6 q^{13} + 4 q^{15} - 2 q^{17} + 2 q^{19} + O(q^{20})\) 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 478864.a

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
478864.a1 478864a1 \([0, 1, 0, -1715929, -865634250]\) \(1302642688/173\) \(74206629223222352\) \([2]\) \(7362288\) \(2.2566\) \(\Gamma_0(N)\)-optimal
478864.a2 478864a2 \([0, 1, 0, -1566284, -1022641784]\) \(-61918288/29929\) \(-205403949689879470336\) \([2]\) \(14724576\) \(2.6032\)