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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 4650m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4650.b2 | 4650m1 | \([1, 1, 0, -2375, -71475]\) | \(-2372030262025/2061298872\) | \(-1288311795000\) | \([]\) | \(7200\) | \(1.0210\) | \(\Gamma_0(N)\)-optimal |
4650.b1 | 4650m2 | \([1, 1, 0, -35700, 7794000]\) | \(-12882119799145/59982446592\) | \(-23430643200000000\) | \([]\) | \(36000\) | \(1.8258\) |
Rank
sage: E.rank()
The elliptic curves in class 4650m have rank \(1\).
Complex multiplication
The elliptic curves in class 4650m do not have complex multiplication.Modular form 4650.2.a.m
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.