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SageMath
E = EllipticCurve("iq1")
E.isogeny_class()
Elliptic curves in class 177450iq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177450.bm2 | 177450iq1 | \([1, 1, 0, 103425, -997875]\) | \(2595575/1512\) | \(-71270851640625000\) | \([]\) | \(2527200\) | \(1.9232\) | \(\Gamma_0(N)\)-optimal |
177450.bm1 | 177450iq2 | \([1, 1, 0, -1480950, -734563500]\) | \(-7620530425/526848\) | \(-24833932305000000000\) | \([]\) | \(7581600\) | \(2.4725\) |
Rank
sage: E.rank()
The elliptic curves in class 177450iq have rank \(0\).
Complex multiplication
The elliptic curves in class 177450iq do not have complex multiplication.Modular form 177450.2.a.iq
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.