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Properties

Label 272734.m
Number of curves $2$
Conductor $272734$
CM no
Rank $1$
Graph

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

Elliptic curves in class 272734.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272734.m1 272734m2 \([1, 1, 0, -1944835, -1095880309]\) \(-3903264618625/226719878\) \(-47253496586247709142\) \([]\) \(7464960\) \(2.5314\)  
272734.m2 272734m1 \([1, 1, 0, 130315, -2608283]\) \(1174241375/694232\) \(-144693485773946648\) \([]\) \(2488320\) \(1.9821\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 272734.m have rank \(1\).

Complex multiplication

The elliptic curves in class 272734.m do not have complex multiplication.

Modular form 272734.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} - 2 q^{9} - q^{12} - 4 q^{13} + q^{16} - 6 q^{17} + 2 q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.