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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1152.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1152.f1 | 1152c2 | \([0, 0, 0, -216, 864]\) | \(3456\) | \(322486272\) | \([2]\) | \(384\) | \(0.33888\) | |
| 1152.f2 | 1152c1 | \([0, 0, 0, -81, -270]\) | \(23328\) | \(2519424\) | \([2]\) | \(192\) | \(-0.0076923\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1152.f have rank \(1\).
Complex multiplication
The elliptic curves in class 1152.f do not have complex multiplication.Modular form 1152.2.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 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.
