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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 100800.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.d1 | 100800pd2 | \([0, 0, 0, -201900, -36945200]\) | \(-7620530425/526848\) | \(-62926387937280000\) | \([]\) | \(995328\) | \(1.9743\) | |
100800.d2 | 100800pd1 | \([0, 0, 0, 14100, -52400]\) | \(2595575/1512\) | \(-180592312320000\) | \([]\) | \(331776\) | \(1.4250\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100800.d have rank \(2\).
Complex multiplication
The elliptic curves in class 100800.d do not have complex multiplication.Modular form 100800.2.a.d
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.