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Properties

Label 1155.m
Number of curves $4$
Conductor $1155$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1155.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1155.m1 1155l3 \([1, 0, 1, -575018, 167782133]\) \(21026497979043461623321/161783881875\) \(161783881875\) \([4]\) \(7680\) \(1.7433\)  
1155.m2 1155l2 \([1, 0, 1, -35963, 2615681]\) \(5143681768032498601/14238434358225\) \(14238434358225\) \([2, 2]\) \(3840\) \(1.3967\)  
1155.m3 1155l4 \([1, 0, 1, -21788, 4702241]\) \(-1143792273008057401/8897444448004035\) \(-8897444448004035\) \([2]\) \(7680\) \(1.7433\)  
1155.m4 1155l1 \([1, 0, 1, -3158, 4403]\) \(3481467828171481/2005331497785\) \(2005331497785\) \([2]\) \(1920\) \(1.0501\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1155.m have rank \(0\).

Complex multiplication

The elliptic curves in class 1155.m do not have complex multiplication.

Modular form 1155.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + q^{7} - 3 q^{8} + q^{9} + q^{10} - q^{11} - q^{12} + 6 q^{13} + q^{14} + q^{15} - q^{16} + 2 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.