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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 77280.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77280.u1 | 77280g4 | \([0, -1, 0, -20280, 1116900]\) | \(1801685643226568/2795664375\) | \(1431380160000\) | \([4]\) | \(163840\) | \(1.2314\) | |
77280.u2 | 77280g3 | \([0, -1, 0, -15825, -756063]\) | \(107009507066176/793349235\) | \(3249558466560\) | \([2]\) | \(163840\) | \(1.2314\) | |
77280.u3 | 77280g1 | \([0, -1, 0, -1650, 6552]\) | \(7767097430464/4251692025\) | \(272108289600\) | \([2, 2]\) | \(81920\) | \(0.88485\) | \(\Gamma_0(N)\)-optimal |
77280.u4 | 77280g2 | \([0, -1, 0, 6400, 45192]\) | \(56614257100792/34652610405\) | \(-17742136527360\) | \([2]\) | \(163840\) | \(1.2314\) |
Rank
sage: E.rank()
The elliptic curves in class 77280.u have rank \(1\).
Complex multiplication
The elliptic curves in class 77280.u do not have complex multiplication.Modular form 77280.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.