Properties

Label 270480.m
Number of curves $2$
Conductor $270480$
CM no
Rank $1$
Graph

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

Elliptic curves in class 270480.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.m1 270480m1 \([0, -1, 0, -243637536, 1463697620736]\) \(1138419279070642590770503/112678869663744000\) \(158305698998944530432000\) \([2]\) \(46448640\) \(3.4864\) \(\Gamma_0(N)\)-optimal
270480.m2 270480m2 \([0, -1, 0, -225287456, 1693455302400]\) \(-900079102684529025934663/360857020174848000000\) \(-506978131640208850944000000\) \([2]\) \(92897280\) \(3.8329\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270480.m have rank \(1\).

Complex multiplication

The elliptic curves in class 270480.m do not have complex multiplication.

Modular form 270480.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 2 q^{11} - 2 q^{13} + q^{15} - 4 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.