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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 273600.cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273600.cg1 | 273600cg2 | \([0, 0, 0, -7800300, 8304498000]\) | \(651038076963/7220000\) | \(582087720960000000000\) | \([2]\) | \(17694720\) | \(2.7988\) | |
273600.cg2 | 273600cg1 | \([0, 0, 0, -888300, -114318000]\) | \(961504803/486400\) | \(39214330675200000000\) | \([2]\) | \(8847360\) | \(2.4522\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 273600.cg have rank \(0\).
Complex multiplication
The elliptic curves in class 273600.cg do not have complex multiplication.Modular form 273600.2.a.cg
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.