Properties

Label 15680.dm
Number of curves $2$
Conductor $15680$
CM no
Rank $0$
Graph

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

Elliptic curves in class 15680.dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.dm1 15680dr2 \([0, -1, 0, -10145, -679615]\) \(-8990558521/10485760\) \(-134690174402560\) \([]\) \(48384\) \(1.4052\)  
15680.dm2 15680dr1 \([0, -1, 0, 1055, 17025]\) \(10100279/16000\) \(-205520896000\) \([]\) \(16128\) \(0.85594\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15680.dm have rank \(0\).

Complex multiplication

The elliptic curves in class 15680.dm do not have complex multiplication.

Modular form 15680.2.a.dm

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + q^{5} + q^{9} + 3q^{11} - q^{13} + 2q^{15} + 6q^{17} + q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.