# Properties

 Label 155848.v Number of curves $2$ Conductor $155848$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 155848.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155848.v1 155848n2 $$[0, -1, 0, -59088, -5508292]$$ $$12576878500/1127$$ $$2044466428928$$ $$$$ $$409600$$ $$1.4022$$
155848.v2 155848n1 $$[0, -1, 0, -3428, -98140]$$ $$-9826000/3703$$ $$-1679383138048$$ $$$$ $$204800$$ $$1.0556$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 155848.v have rank $$1$$.

## Complex multiplication

The elliptic curves in class 155848.v do not have complex multiplication.

## Modular form 155848.2.a.v

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{7} + q^{9} - 6q^{13} + O(q^{20})$$ ## 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. 