# Properties

 Label 7942.m Number of curves $2$ Conductor $7942$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 7942.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7942.m1 7942n2 $$[1, 0, 0, -115632, 4256512]$$ $$24928563670864867/13279961395712$$ $$91087255213188608$$ $$[2]$$ $$79200$$ $$1.9456$$
7942.m2 7942n1 $$[1, 0, 0, -66992, -6629120]$$ $$4847659921191907/42218553344$$ $$289577057386496$$ $$[2]$$ $$39600$$ $$1.5990$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7942.m have rank $$0$$.

## Complex multiplication

The elliptic curves in class 7942.m do not have complex multiplication.

## Modular form7942.2.a.m

sage: E.q_eigenform(10)

$$q + q^{2} - 2 q^{3} + q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + q^{8} + q^{9} + 2 q^{10} - q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{14} - 4 q^{15} + q^{16} - 6 q^{17} + q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.