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SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 217800.gh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
217800.gh1 | 217800gm2 | \([0, 0, 0, -37035075, 2617078750]\) | \(102129622/59049\) | \(3248061324386278752000000\) | \([2]\) | \(40550400\) | \(3.3928\) | |
217800.gh2 | 217800gm1 | \([0, 0, 0, -25056075, -48113986250]\) | \(63253004/243\) | \(6683253753881232000000\) | \([2]\) | \(20275200\) | \(3.0463\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 217800.gh have rank \(0\).
Complex multiplication
The elliptic curves in class 217800.gh do not have complex multiplication.Modular form 217800.2.a.gh
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.