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SageMath
E = EllipticCurve("fd1")
E.isogeny_class()
Elliptic curves in class 432450.fd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
432450.fd1 | 432450fd4 | \([1, -1, 1, -137404721480, -19604231344238353]\) | \(28379906689597370652529/1357352437500\) | \(13721776602235504795898437500\) | \([2]\) | \(1592524800\) | \(4.8763\) | |
432450.fd2 | 432450fd3 | \([1, -1, 1, -8573541980, -307381954010353]\) | \(-6894246873502147249/47925198774000\) | \(-484486455415938279555093750000\) | \([2]\) | \(796262400\) | \(4.5298\) | |
432450.fd3 | 432450fd2 | \([1, -1, 1, -1844619980, -21912644858353]\) | \(68663623745397169/19216056254400\) | \(194259371268758747084775000000\) | \([2]\) | \(530841600\) | \(4.3270\) | \(\Gamma_0(N)\)-optimal* |
432450.fd4 | 432450fd1 | \([1, -1, 1, 300332020, -2247724922353]\) | \(296354077829711/387386634240\) | \(-3916177336759816635840000000\) | \([2]\) | \(265420800\) | \(3.9805\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 432450.fd have rank \(0\).
Complex multiplication
The elliptic curves in class 432450.fd do not have complex multiplication.Modular form 432450.2.a.fd
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.