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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 33810.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33810.f1 | 33810d2 | \([1, 1, 0, -403, -3233]\) | \(21184951663/428490\) | \(146972070\) | \([2]\) | \(14336\) | \(0.35823\) | |
33810.f2 | 33810d1 | \([1, 1, 0, -53, 57]\) | \(49430863/20700\) | \(7100100\) | \([2]\) | \(7168\) | \(0.011653\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33810.f have rank \(2\).
Complex multiplication
The elliptic curves in class 33810.f do not have complex multiplication.Modular form 33810.2.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.