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Properties

Label 327600.dm
Number of curves $4$
Conductor $327600$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dm1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 327600.dm have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1\)
\(7\)\(1 + T\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 327600.dm do not have complex multiplication.

Modular form 327600.2.a.dm

Copy content sage:E.q_eigenform(10)
 
\(q - q^{7} - q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 327600.dm

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327600.dm1 327600dm3 \([0, 0, 0, -60744675, 182224633250]\) \(531301262949272089/4740474375\) \(221171572440000000000\) \([2]\) \(23592960\) \(3.0696\)  
327600.dm2 327600dm2 \([0, 0, 0, -3882675, 2711299250]\) \(138742439989609/12224619225\) \(570351834561600000000\) \([2, 2]\) \(11796480\) \(2.7230\)  
327600.dm3 327600dm1 \([0, 0, 0, -840675, -248566750]\) \(1408317602329/242911305\) \(11333269846080000000\) \([2]\) \(5898240\) \(2.3764\) \(\Gamma_0(N)\)-optimal
327600.dm4 327600dm4 \([0, 0, 0, 4307325, 12629389250]\) \(189425802193991/1586486902455\) \(-74019132920940480000000\) \([2]\) \(23592960\) \(3.0696\)