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SageMath
E = EllipticCurve("na1")
E.isogeny_class()
Elliptic curves in class 100800na
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.mw4 | 100800na1 | \([0, 0, 0, -6600, 1339000]\) | \(-2725888/64827\) | \(-756142128000000\) | \([2]\) | \(393216\) | \(1.5356\) | \(\Gamma_0(N)\)-optimal |
100800.mw3 | 100800na2 | \([0, 0, 0, -227100, 41470000]\) | \(6940769488/35721\) | \(6666395904000000\) | \([2, 2]\) | \(786432\) | \(1.8822\) | |
100800.mw2 | 100800na3 | \([0, 0, 0, -353100, -9686000]\) | \(6522128932/3720087\) | \(2777030065152000000\) | \([2]\) | \(1572864\) | \(2.2288\) | |
100800.mw1 | 100800na4 | \([0, 0, 0, -3629100, 2661010000]\) | \(7080974546692/189\) | \(141087744000000\) | \([2]\) | \(1572864\) | \(2.2288\) |
Rank
sage: E.rank()
The elliptic curves in class 100800na have rank \(0\).
Complex multiplication
The elliptic curves in class 100800na do not have complex multiplication.Modular form 100800.2.a.na
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.