Properties

Label 19600.dm
Number of curves $4$
Conductor $19600$
CM no
Rank $1$
Graph

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

Elliptic curves in class 19600.dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19600.dm1 19600co3 \([0, -1, 0, -50633, -4367488]\) \(488095744/125\) \(3676531250000\) \([2]\) \(51840\) \(1.3970\)  
19600.dm2 19600co4 \([0, -1, 0, -44508, -5469988]\) \(-20720464/15625\) \(-7353062500000000\) \([2]\) \(103680\) \(1.7436\)  
19600.dm3 19600co1 \([0, -1, 0, -1633, 18012]\) \(16384/5\) \(147061250000\) \([2]\) \(17280\) \(0.84772\) \(\Gamma_0(N)\)-optimal
19600.dm4 19600co2 \([0, -1, 0, 4492, 116012]\) \(21296/25\) \(-11764900000000\) \([2]\) \(34560\) \(1.1943\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19600.dm have rank \(1\).

Complex multiplication

The elliptic curves in class 19600.dm do not have complex multiplication.

Modular form 19600.2.a.dm

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{9} + 2 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.