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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 6018.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6018.a1 | 6018c2 | \([1, 1, 0, -10327, -407435]\) | \(121818136413690361/289971215712\) | \(289971215712\) | \([2]\) | \(17280\) | \(1.0789\) | |
6018.a2 | 6018c1 | \([1, 1, 0, -887, -1515]\) | \(77314220407801/44175393792\) | \(44175393792\) | \([2]\) | \(8640\) | \(0.73238\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6018.a have rank \(2\).
Complex multiplication
The elliptic curves in class 6018.a do not have complex multiplication.Modular form 6018.2.a.a
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.