# Properties

 Label 1155.c Number of curves $2$ Conductor $1155$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("c1")

E.isogeny_class()

## Elliptic curves in class 1155.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1155.c1 1155n2 $$[0, 1, 1, -26790, -31917424]$$ $$-2126464142970105856/438611057788643355$$ $$-438611057788643355$$ $$[]$$ $$30000$$ $$2.0645$$
1155.c2 1155n1 $$[0, 1, 1, -8940, 378056]$$ $$-79028701534867456/16987307596875$$ $$-16987307596875$$ $$$$ $$6000$$ $$1.2598$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1155.c have rank $$1$$.

## Complex multiplication

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

## Modular form1155.2.a.c

sage: E.q_eigenform(10)

$$q - 2 q^{2} + q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + q^{7} + q^{9} - 2 q^{10} + q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{14} + q^{15} - 4 q^{16} - 7 q^{17} - 2 q^{18} - 5 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 