Properties

Label 53312c
Number of curves $1$
Conductor $53312$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 53312c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53312.y1 53312c1 \([0, -1, 0, -853841, 426823153]\) \(-728871512656/410338673\) \(-38756692663485612032\) \([]\) \(1806336\) \(2.4619\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53312c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 53312c do not have complex multiplication.

Modular form 53312.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4 q^{5} - 2 q^{9} + 3 q^{11} + 5 q^{13} - 4 q^{15} - q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display