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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 177600dd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177600.g1 | 177600dd1 | \([0, -1, 0, -933, -2763]\) | \(5619712/2997\) | \(47952000000\) | \([2]\) | \(196608\) | \(0.74078\) | \(\Gamma_0(N)\)-optimal |
177600.g2 | 177600dd2 | \([0, -1, 0, 3567, -25263]\) | \(19600688/12321\) | \(-3154176000000\) | \([2]\) | \(393216\) | \(1.0874\) |
Rank
sage: E.rank()
The elliptic curves in class 177600dd have rank \(2\).
Complex multiplication
The elliptic curves in class 177600dd do not have complex multiplication.Modular form 177600.2.a.dd
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.