# Properties

 Label 7400.b Number of curves $2$ Conductor $7400$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("b1")

E.isogeny_class()

## Elliptic curves in class 7400.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7400.b1 7400j1 $$[0, 1, 0, -1208, 9088]$$ $$97556/37$$ $$74000000000$$ $$[2]$$ $$7040$$ $$0.78504$$ $$\Gamma_0(N)$$-optimal
7400.b2 7400j2 $$[0, 1, 0, 3792, 69088]$$ $$1507142/1369$$ $$-5476000000000$$ $$[2]$$ $$14080$$ $$1.1316$$

## Rank

sage: E.rank()

The elliptic curves in class 7400.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 7400.b do not have complex multiplication.

## Modular form7400.2.a.b

sage: E.q_eigenform(10)

$$q - 2 q^{3} + 4 q^{7} + q^{9} + 4 q^{11} - 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.