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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 57600dh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57600.b2 | 57600dh1 | \([0, 0, 0, -750, 34000]\) | \(-8000/81\) | \(-472392000000\) | \([2]\) | \(73728\) | \(0.92231\) | \(\Gamma_0(N)\)-optimal |
57600.b1 | 57600dh2 | \([0, 0, 0, -21000, 1168000]\) | \(2744000/9\) | \(3359232000000\) | \([2]\) | \(147456\) | \(1.2689\) |
Rank
sage: E.rank()
The elliptic curves in class 57600dh have rank \(1\).
Complex multiplication
The elliptic curves in class 57600dh do not have complex multiplication.Modular form 57600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.