# Properties

 Label 51600.bv Number of curves $4$ Conductor $51600$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("bv1")

sage: E.isogeny_class()

## Elliptic curves in class 51600.bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.bv1 51600bw4 $$[0, -1, 0, -2201608, 1258089712]$$ $$18440127492397057/1032$$ $$66048000000$$ $$$$ $$737280$$ $$1.9909$$
51600.bv2 51600bw2 $$[0, -1, 0, -137608, 19689712]$$ $$4502751117697/1065024$$ $$68161536000000$$ $$[2, 2]$$ $$368640$$ $$1.6444$$
51600.bv3 51600bw3 $$[0, -1, 0, -121608, 24425712]$$ $$-3107661785857/2215383048$$ $$-141784515072000000$$ $$$$ $$737280$$ $$1.9909$$
51600.bv4 51600bw1 $$[0, -1, 0, -9608, 233712]$$ $$1532808577/528384$$ $$33816576000000$$ $$$$ $$184320$$ $$1.2978$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 51600.bv have rank $$0$$.

## Complex multiplication

The elliptic curves in class 51600.bv do not have complex multiplication.

## Modular form 51600.2.a.bv

sage: E.q_eigenform(10)

$$q - q^{3} + 4q^{7} + q^{9} - 4q^{11} - 6q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 