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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 35280dh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.er4 | 35280dh1 | \([0, 0, 0, -17052, 856471]\) | \(10788913152/8575\) | \(435818955600\) | \([2]\) | \(55296\) | \(1.1637\) | \(\Gamma_0(N)\)-optimal |
35280.er3 | 35280dh2 | \([0, 0, 0, -20727, 460306]\) | \(1210991472/588245\) | \(478354885666560\) | \([2]\) | \(110592\) | \(1.5103\) | |
35280.er2 | 35280dh3 | \([0, 0, 0, -58212, -4454541]\) | \(588791808/109375\) | \(4052449217250000\) | \([2]\) | \(165888\) | \(1.7130\) | |
35280.er1 | 35280dh4 | \([0, 0, 0, -885087, -320486166]\) | \(129348709488/6125\) | \(3630994498656000\) | \([2]\) | \(331776\) | \(2.0596\) |
Rank
sage: E.rank()
The elliptic curves in class 35280dh have rank \(0\).
Complex multiplication
The elliptic curves in class 35280dh do not have complex multiplication.Modular form 35280.2.a.dh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.