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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 108900.cr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
108900.cr1 | 108900bs2 | \([0, 0, 0, -11879175, 15764696750]\) | \(-296587984/125\) | \(-78133812124500000000\) | \([]\) | \(3421440\) | \(2.7782\) | |
108900.cr2 | 108900bs1 | \([0, 0, 0, 99825, 84185750]\) | \(176/5\) | \(-3125352484980000000\) | \([]\) | \(1140480\) | \(2.2289\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 108900.cr have rank \(0\).
Complex multiplication
The elliptic curves in class 108900.cr do not have complex multiplication.Modular form 108900.2.a.cr
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.