Properties

Label 39600dm
Number of curves $4$
Conductor $39600$
CM no
Rank $1$
Graph

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

Elliptic curves in class 39600dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39600.e3 39600dm1 \([0, 0, 0, -9300, 451375]\) \(-488095744/200475\) \(-36536568750000\) \([2]\) \(110592\) \(1.3108\) \(\Gamma_0(N)\)-optimal
39600.e2 39600dm2 \([0, 0, 0, -161175, 24903250]\) \(158792223184/16335\) \(47632860000000\) \([2]\) \(221184\) \(1.6573\)  
39600.e4 39600dm3 \([0, 0, 0, 71700, -4935125]\) \(223673040896/187171875\) \(-34112074218750000\) \([2]\) \(331776\) \(1.8601\)  
39600.e1 39600dm4 \([0, 0, 0, -350175, -43325750]\) \(1628514404944/664335375\) \(1937201953500000000\) \([2]\) \(663552\) \(2.2066\)  

Rank

sage: E.rank()
 

The elliptic curves in class 39600dm have rank \(1\).

Complex multiplication

The elliptic curves in class 39600dm do not have complex multiplication.

Modular form 39600.2.a.dm

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} - q^{11} + 4 q^{13} - 6 q^{17} - 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.