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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 7728.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7728.q1 | 7728e2 | \([0, 1, 0, -30728, 2061972]\) | \(1566789944863250/925924041\) | \(1896292435968\) | \([2]\) | \(21504\) | \(1.3005\) | |
7728.q2 | 7728e1 | \([0, 1, 0, -1568, 44100]\) | \(-416618810500/598934007\) | \(-613308423168\) | \([2]\) | \(10752\) | \(0.95392\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7728.q have rank \(1\).
Complex multiplication
The elliptic curves in class 7728.q do not have complex multiplication.Modular form 7728.2.a.q
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.