# Properties

 Label 74256.b Number of curves $2$ Conductor $74256$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 74256.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
74256.b1 74256bw1 $$[0, -1, 0, -7280, -236544]$$ $$10418796526321/6390657$$ $$26176131072$$ $$$$ $$143360$$ $$0.94179$$ $$\Gamma_0(N)$$-optimal
74256.b2 74256bw2 $$[0, -1, 0, -5920, -329024]$$ $$-5602762882081/8312741073$$ $$-34048987435008$$ $$$$ $$286720$$ $$1.2884$$

## Rank

sage: E.rank()

The elliptic curves in class 74256.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 74256.b do not have complex multiplication.

## Modular form 74256.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{5} - q^{7} + q^{9} + 4q^{11} + q^{13} + 4q^{15} + q^{17} + O(q^{20})$$ ## 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. 