Properties

Label 80275.m
Number of curves $3$
Conductor $80275$
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 80275.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80275.m1 80275a3 \([0, -1, 1, -3250433, -2254505732]\) \(-50357871050752/19\) \(-1432958921875\) \([]\) \(699840\) \(2.1206\)  
80275.m2 80275a2 \([0, -1, 1, -39433, -3193357]\) \(-89915392/6859\) \(-517298170796875\) \([]\) \(233280\) \(1.5713\)  
80275.m3 80275a1 \([0, -1, 1, 2817, -3482]\) \(32768/19\) \(-1432958921875\) \([]\) \(77760\) \(1.0220\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 80275.m have rank \(1\).

Complex multiplication

The elliptic curves in class 80275.m do not have complex multiplication.

Modular form 80275.2.a.m

sage: E.q_eigenform(10)
 
\(q + 2q^{3} - 2q^{4} - q^{7} + q^{9} - 3q^{11} - 4q^{12} + 4q^{16} + 3q^{17} - q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.