# Properties

 Label 31200.cb Number of curves $4$ Conductor $31200$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cb1")

sage: E.isogeny_class()

## Elliptic curves in class 31200.cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.cb1 31200n4 $$[0, 1, 0, -93608, -11054712]$$ $$11339065490696/351$$ $$2808000000$$ $$[2]$$ $$98304$$ $$1.3174$$
31200.cb2 31200n3 $$[0, 1, 0, -9233, 45663]$$ $$1360251712/771147$$ $$49353408000000$$ $$[2]$$ $$98304$$ $$1.3174$$
31200.cb3 31200n1 $$[0, 1, 0, -5858, -173712]$$ $$22235451328/123201$$ $$123201000000$$ $$[2, 2]$$ $$49152$$ $$0.97086$$ $$\Gamma_0(N)$$-optimal
31200.cb4 31200n2 $$[0, 1, 0, -2608, -362212]$$ $$-245314376/6908733$$ $$-55269864000000$$ $$[2]$$ $$98304$$ $$1.3174$$

## Rank

sage: E.rank()

The elliptic curves in class 31200.cb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 31200.cb do not have complex multiplication.

## Modular form 31200.2.a.cb

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} + 4q^{11} - q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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 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.