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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 4830.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4830.q1 | 4830p2 | \([1, 0, 1, -423, 1828]\) | \(8341959848041/3327411150\) | \(3327411150\) | \([2]\) | \(3840\) | \(0.52532\) | |
4830.q2 | 4830p1 | \([1, 0, 1, -193, -1024]\) | \(789145184521/17996580\) | \(17996580\) | \([2]\) | \(1920\) | \(0.17875\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4830.q have rank \(1\).
Complex multiplication
The elliptic curves in class 4830.q do not have complex multiplication.Modular form 4830.2.a.q
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.