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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 7200f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7200.z3 | 7200f1 | \([0, 0, 0, -2325, 38500]\) | \(1906624/225\) | \(164025000000\) | \([2, 2]\) | \(6144\) | \(0.88325\) | \(\Gamma_0(N)\)-optimal |
7200.z2 | 7200f2 | \([0, 0, 0, -9075, -292250]\) | \(14172488/1875\) | \(10935000000000\) | \([2]\) | \(12288\) | \(1.2298\) | |
7200.z1 | 7200f3 | \([0, 0, 0, -36075, 2637250]\) | \(890277128/15\) | \(87480000000\) | \([2]\) | \(12288\) | \(1.2298\) | |
7200.z4 | 7200f4 | \([0, 0, 0, 3300, 196000]\) | \(85184/405\) | \(-18895680000000\) | \([2]\) | \(12288\) | \(1.2298\) |
Rank
sage: E.rank()
The elliptic curves in class 7200f have rank \(0\).
Complex multiplication
The elliptic curves in class 7200f do not have complex multiplication.Modular form 7200.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.