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Properties

Label 439824.a
Number of curves $2$
Conductor $439824$
CM no
Rank $1$
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 439824.a have rank \(1\).

Complex multiplication

The elliptic curves in class 439824.a do not have complex multiplication.

Modular form 439824.2.a.a

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{5} + q^{9} - q^{11} - 2 q^{13} + 4 q^{15} + q^{17} - 2 q^{19} + O(q^{20})\) 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 439824.a

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
439824.a1 439824a1 \([0, -1, 0, -3740, 43296]\) \(192143824/85833\) \(2585130653952\) \([2]\) \(1105920\) \(1.0772\) \(\Gamma_0(N)\)-optimal
439824.a2 439824a2 \([0, -1, 0, 12920, 309856]\) \(1979654684/1499553\) \(-180655012758528\) \([2]\) \(2211840\) \(1.4238\)