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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 14400br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14400.fg3 | 14400br1 | \([0, 0, 0, -202575, -35093500]\) | \(1261112198464/675\) | \(492075000000\) | \([2]\) | \(73728\) | \(1.5731\) | \(\Gamma_0(N)\)-optimal |
14400.fg2 | 14400br2 | \([0, 0, 0, -203700, -34684000]\) | \(20034997696/455625\) | \(21257640000000000\) | \([2, 2]\) | \(147456\) | \(1.9197\) | |
14400.fg1 | 14400br3 | \([0, 0, 0, -446700, 63974000]\) | \(26410345352/10546875\) | \(3936600000000000000\) | \([2]\) | \(294912\) | \(2.2662\) | |
14400.fg4 | 14400br4 | \([0, 0, 0, 21300, -107134000]\) | \(2863288/13286025\) | \(-4958982259200000000\) | \([2]\) | \(294912\) | \(2.2662\) |
Rank
sage: E.rank()
The elliptic curves in class 14400br have rank \(0\).
Complex multiplication
The elliptic curves in class 14400br do not have complex multiplication.Modular form 14400.2.a.br
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 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
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.