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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 48960.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48960.f1 | 48960bs1 | \([0, 0, 0, -1008, -12312]\) | \(151732224/85\) | \(63452160\) | \([2]\) | \(24576\) | \(0.44433\) | \(\Gamma_0(N)\)-optimal |
48960.f2 | 48960bs2 | \([0, 0, 0, -828, -16848]\) | \(-5256144/7225\) | \(-86294937600\) | \([2]\) | \(49152\) | \(0.79091\) |
Rank
sage: E.rank()
The elliptic curves in class 48960.f have rank \(0\).
Complex multiplication
The elliptic curves in class 48960.f do not have complex multiplication.Modular form 48960.2.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.