Properties

Label 48400.w
Number of curves $4$
Conductor $48400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 48400.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48400.w1 48400cp4 \([0, 1, 0, -21478508, -38320869512]\) \(154639330142416/33275\) \(235794769100000000\) \([2]\) \(2488320\) \(2.7181\)  
48400.w2 48400cp3 \([0, 1, 0, -1347133, -594672762]\) \(610462990336/8857805\) \(3923035470901250000\) \([2]\) \(1244160\) \(2.3715\)  
48400.w3 48400cp2 \([0, 1, 0, -303508, -36469512]\) \(436334416/171875\) \(1217948187500000000\) \([2]\) \(829440\) \(2.1688\)  
48400.w4 48400cp1 \([0, 1, 0, -137133, 19099738]\) \(643956736/15125\) \(6698715031250000\) \([2]\) \(414720\) \(1.8222\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 48400.w have rank \(1\).

Complex multiplication

The elliptic curves in class 48400.w do not have complex multiplication.

Modular form 48400.2.a.w

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + 4 q^{7} + q^{9} - 4 q^{13} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.