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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 7728q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7728.m2 | 7728q1 | \([0, 1, 0, 280, 564]\) | \(590589719/365148\) | \(-1495646208\) | \([2]\) | \(4608\) | \(0.44961\) | \(\Gamma_0(N)\)-optimal |
7728.m1 | 7728q2 | \([0, 1, 0, -1160, 3444]\) | \(42180533641/22862322\) | \(93644070912\) | \([2]\) | \(9216\) | \(0.79619\) |
Rank
sage: E.rank()
The elliptic curves in class 7728q have rank \(1\).
Complex multiplication
The elliptic curves in class 7728q 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 Cremona 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 Cremona labels.