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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 54150.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54150.u1 | 54150x4 | \([1, 0, 1, -67484626, 206046130148]\) | \(46237740924063961/1806561830400\) | \(1327988951439696600000000\) | \([2]\) | \(7464960\) | \(3.3960\) | |
54150.u2 | 54150x2 | \([1, 0, 1, -9950251, -11995613602]\) | \(148212258825961/1218375000\) | \(895617582240234375000\) | \([2]\) | \(2488320\) | \(2.8467\) | |
54150.u3 | 54150x1 | \([1, 0, 1, -203251, -435671602]\) | \(-1263214441/110808000\) | \(-81454062216375000000\) | \([2]\) | \(1244160\) | \(2.5002\) | \(\Gamma_0(N)\)-optimal |
54150.u4 | 54150x3 | \([1, 0, 1, 1827374, 11695282148]\) | \(918046641959/80912056320\) | \(-59477796454625280000000\) | \([2]\) | \(3732480\) | \(3.0495\) |
Rank
sage: E.rank()
The elliptic curves in class 54150.u have rank \(1\).
Complex multiplication
The elliptic curves in class 54150.u do not have complex multiplication.Modular form 54150.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.