Properties

Label 72450.m
Number of curves $2$
Conductor $72450$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72450.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.m1 72450bf2 \([1, -1, 0, -95067, -6265409]\) \(8341959848041/3327411150\) \(37901292630468750\) \([2]\) \(737280\) \(1.8793\)  
72450.m2 72450bf1 \([1, -1, 0, -43317, 3411841]\) \(789145184521/17996580\) \(204992294062500\) \([2]\) \(368640\) \(1.5328\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 72450.m have rank \(1\).

Complex multiplication

The elliptic curves in class 72450.m do not have complex multiplication.

Modular form 72450.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} - 2q^{11} + 2q^{13} + q^{14} + q^{16} - 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.