# Properties

 Label 142912.bm Number of curves $4$ Conductor $142912$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bm1")

sage: E.isogeny_class()

## Elliptic curves in class 142912.bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
142912.bm1 142912p4 $$[0, 0, 0, -3414764, -2428519088]$$ $$16798320881842096017/2132227789307$$ $$558950721600094208$$ $$[2]$$ $$2752512$$ $$2.4272$$
142912.bm2 142912p3 $$[0, 0, 0, -1354604, 582039120]$$ $$1048626554636928177/48569076788309$$ $$12732092065594474496$$ $$[2]$$ $$2752512$$ $$2.4272$$
142912.bm3 142912p2 $$[0, 0, 0, -231724, -31053360]$$ $$5249244962308257/1448621666569$$ $$379747478161063936$$ $$[2, 2]$$ $$1376256$$ $$2.0807$$
142912.bm4 142912p1 $$[0, 0, 0, 37396, -3172528]$$ $$22062729659823/29354283343$$ $$-7695049252667392$$ $$[2]$$ $$688128$$ $$1.7341$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 142912.bm have rank $$1$$.

## Complex multiplication

The elliptic curves in class 142912.bm do not have complex multiplication.

## Modular form 142912.2.a.bm

sage: E.q_eigenform(10)

$$q + 2q^{5} + q^{7} - 3q^{9} - q^{11} - 6q^{13} - 2q^{17} - 8q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.