# Properties

 Label 47915.b Number of curves $3$ Conductor $47915$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 47915.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47915.b1 47915c3 $$[0, 1, 1, -179795, -30756119]$$ $$-250523582464/13671875$$ $$-35078290748046875$$ $$[]$$ $$311040$$ $$1.9329$$
47915.b2 47915c1 $$[0, 1, 1, -1825, 32691]$$ $$-262144/35$$ $$-89800424315$$ $$[]$$ $$34560$$ $$0.83431$$ $$\Gamma_0(N)$$-optimal
47915.b3 47915c2 $$[0, 1, 1, 11865, -80936]$$ $$71991296/42875$$ $$-110005519785875$$ $$[]$$ $$103680$$ $$1.3836$$

## Rank

sage: E.rank()

The elliptic curves in class 47915.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 47915.b do not have complex multiplication.

## Modular form 47915.2.a.b

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{4} + q^{5} + q^{7} - 2q^{9} - 3q^{11} - 2q^{12} - 5q^{13} + q^{15} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.