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Label Class Conductor Rank Torsion CM Regulator Weierstrass coefficients Weierstrass equation
57.a1 57.a \( 3 \cdot 19 \) $1$ $\mathsf{trivial}$ $0.037574592$ $[0, -1, 1, -2, 2]$ \(y^2+y=x^3-x^2-2x+2\)
57.b1 57.b \( 3 \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[0, 1, 1, -4390, -113432]$ \(y^2+y=x^3+x^2-4390x-113432\)
57.b2 57.b \( 3 \cdot 19 \) $0$ $\Z/5\Z$ $1$ $[0, 1, 1, 20, -32]$ \(y^2+y=x^3+x^2+20x-32\)
57.c1 57.c \( 3 \cdot 19 \) $0$ $\Z/4\Z$ $1$ $[1, 0, 1, -102, 385]$ \(y^2+xy+y=x^3-102x+385\)
57.c2 57.c \( 3 \cdot 19 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 0, 1, -7, 5]$ \(y^2+xy+y=x^3-7x+5\)
57.c3 57.c \( 3 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -2, -1]$ \(y^2+xy+y=x^3-2x-1\)
57.c4 57.c \( 3 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, 8, 29]$ \(y^2+xy+y=x^3+8x+29\)
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