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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 57015f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57015.d3 | 57015f1 | \([0, 0, 1, -1869348, 2307599703]\) | \(-990984032431410774016/2582079138529296875\) | \(-1882335691987857421875\) | \([]\) | \(2080080\) | \(2.7699\) | \(\Gamma_0(N)\)-optimal |
57015.d2 | 57015f2 | \([0, 0, 1, -202524348, 1109339370828]\) | \(-1260166446752151291924054016/1507563389523597875\) | \(-1099013710962702850875\) | \([3]\) | \(6240240\) | \(3.3192\) | |
57015.d1 | 57015f3 | \([0, 0, 1, -16404476898, 808707913727283]\) | \(-669704693478538248257181174562816/1146635\) | \(-835896915\) | \([3]\) | \(18720720\) | \(3.8685\) |
Rank
sage: E.rank()
The elliptic curves in class 57015f have rank \(0\).
Complex multiplication
The elliptic curves in class 57015f do not have complex multiplication.Modular form 57015.2.a.f
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.