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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 14400.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14400.j1 | 14400bu3 | \([0, 0, 0, -446700, -63974000]\) | \(26410345352/10546875\) | \(3936600000000000000\) | \([2]\) | \(294912\) | \(2.2662\) | |
14400.j2 | 14400bu2 | \([0, 0, 0, -203700, 34684000]\) | \(20034997696/455625\) | \(21257640000000000\) | \([2, 2]\) | \(147456\) | \(1.9197\) | |
14400.j3 | 14400bu1 | \([0, 0, 0, -202575, 35093500]\) | \(1261112198464/675\) | \(492075000000\) | \([2]\) | \(73728\) | \(1.5731\) | \(\Gamma_0(N)\)-optimal |
14400.j4 | 14400bu4 | \([0, 0, 0, 21300, 107134000]\) | \(2863288/13286025\) | \(-4958982259200000000\) | \([2]\) | \(294912\) | \(2.2662\) |
Rank
sage: E.rank()
The elliptic curves in class 14400.j have rank \(0\).
Complex multiplication
The elliptic curves in class 14400.j do not have complex multiplication.Modular form 14400.2.a.j
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.