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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 18480de
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18480.cv1 | 18480de1 | \([0, 1, 0, -79920, 8669268]\) | \(13782741913468081/701662500\) | \(2874009600000\) | \([2]\) | \(69120\) | \(1.4606\) | \(\Gamma_0(N)\)-optimal |
18480.cv2 | 18480de2 | \([0, 1, 0, -75600, 9652500]\) | \(-11666347147400401/3126621093750\) | \(-12806640000000000\) | \([2]\) | \(138240\) | \(1.8071\) |
Rank
sage: E.rank()
The elliptic curves in class 18480de have rank \(1\).
Complex multiplication
The elliptic curves in class 18480de do not have complex multiplication.Modular form 18480.2.a.de
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.