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Properties

Label 213150.dm
Number of curves $2$
Conductor $213150$
CM no
Rank $0$
Graph

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

Elliptic curves in class 213150.dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
213150.dm1 213150gz2 \([1, 0, 1, -7976001, 8694831898]\) \(-30526075007211889/103499257854\) \(-190259127926019468750\) \([]\) \(10372320\) \(2.7553\)  
213150.dm2 213150gz1 \([1, 0, 1, -1251, -5877602]\) \(-117649/8118144\) \(-14923305054000000\) \([]\) \(1481760\) \(1.7824\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 213150.dm have rank \(0\).

Complex multiplication

The elliptic curves in class 213150.dm do not have complex multiplication.

Modular form 213150.2.a.dm

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} - 2 q^{11} + q^{12} + q^{16} - 3 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.