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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 57960o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57960.t4 | 57960o1 | \([0, 0, 0, 13497, -659878]\) | \(1457028215984/1851148215\) | \(-345468684476160\) | \([2]\) | \(196608\) | \(1.4756\) | \(\Gamma_0(N)\)-optimal |
| 57960.t3 | 57960o2 | \([0, 0, 0, -81723, -6392122]\) | \(80859142234084/23148101025\) | \(17279964822758400\) | \([2, 2]\) | \(393216\) | \(1.8222\) | |
| 57960.t2 | 57960o3 | \([0, 0, 0, -487443, 125953742]\) | \(8579021289461282/374333754375\) | \(558877300611840000\) | \([2]\) | \(786432\) | \(2.1688\) | |
| 57960.t1 | 57960o4 | \([0, 0, 0, -1199523, -505601602]\) | \(127847420666360642/17899707105\) | \(26724119510108160\) | \([2]\) | \(786432\) | \(2.1688\) |
Rank
sage: E.rank()
The elliptic curves in class 57960o have rank \(1\).
Complex multiplication
The elliptic curves in class 57960o do not have complex multiplication.Modular form 57960.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
