Properties

 Label 98315i Number of curves $3$ Conductor $98315$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

Elliptic curves in class 98315i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
98315.e2 98315i1 $$[0, -1, 1, -3745, 99121]$$ $$-262144/35$$ $$-775752639515$$ $$[]$$ $$96096$$ $$1.0140$$ $$\Gamma_0(N)$$-optimal
98315.e3 98315i2 $$[0, -1, 1, 24345, -257622]$$ $$71991296/42875$$ $$-950296983405875$$ $$[]$$ $$288288$$ $$1.5633$$
98315.e1 98315i3 $$[0, -1, 1, -368915, -90097869]$$ $$-250523582464/13671875$$ $$-303028374810546875$$ $$[]$$ $$864864$$ $$2.1126$$

Rank

sage: E.rank()

The elliptic curves in class 98315i have rank $$1$$.

Complex multiplication

The elliptic curves in class 98315i do not have complex multiplication.

Modular form 98315.2.a.i

sage: E.q_eigenform(10)

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels. 