# Properties

 Label 152460l Number of curves $4$ Conductor $152460$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 152460l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152460.bc3 152460l1 $$[0, 0, 0, -2898192, 1927196161]$$ $$-130287139815424/2250652635$$ $$-46506332599167173040$$ $$[2]$$ $$4976640$$ $$2.5718$$ $$\Gamma_0(N)$$-optimal
152460.bc2 152460l2 $$[0, 0, 0, -46561647, 122289876214]$$ $$33766427105425744/9823275$$ $$3247729923373689600$$ $$[2]$$ $$9953280$$ $$2.9184$$
152460.bc4 152460l3 $$[0, 0, 0, 11215248, 9235488229]$$ $$7549996227362816/6152409907875$$ $$-127130245250860853694000$$ $$[2]$$ $$14929920$$ $$3.1211$$
152460.bc1 152460l4 $$[0, 0, 0, -54010407, 80553219406]$$ $$52702650535889104/22020583921875$$ $$7280352971207157996000000$$ $$[2]$$ $$29859840$$ $$3.4677$$

## Rank

sage: E.rank()

The elliptic curves in class 152460l have rank $$1$$.

## Complex multiplication

The elliptic curves in class 152460l do not have complex multiplication.

## Modular form 152460.2.a.l

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} - 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.