Elliptic curve isogeny class with Cremona label 12495p (LMFDB label 12495.n)

• Label: 12495p
• Number of curves: $4$
• Conductor: $12495$
• CM: no
• Rank: $1$

Elliptic curves in class 12495p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12495.n4	12495p1	\([1, 0, 1, 1542, 31063]\)	\(3449795831/5510295\)	\(-648280696455\)	\([2]\)	\(18432\)	\(0.95164\)	\(\Gamma_0(N)\)-optimal
12495.n3	12495p2	\([1, 0, 1, -10463, 314381]\)	\(1076575468249/258084225\)	\(30363350987025\)	\([2, 2]\)	\(36864\)	\(1.2982\)
12495.n2	12495p3	\([1, 0, 1, -56768, -4945867]\)	\(171963096231529/9865918125\)	\(1160715401488125\)	\([2]\)	\(73728\)	\(1.6448\)
12495.n1	12495p4	\([1, 0, 1, -156238, 23755001]\)	\(3585019225176649/316207395\)	\(37201483814355\)	\([4]\)	\(73728\)	\(1.6448\)

Rank

The elliptic curves in class 12495p have rank \(1\).

Complex multiplication

The elliptic curves in class 12495p do not have complex multiplication.

Modular form 12495.2.a.p

Isogeny 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.