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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 4830.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4830.g1 | 4830f2 | \([1, 1, 0, -9177, 75141]\) | \(85486955243540761/46777901234400\) | \(46777901234400\) | \([2]\) | \(12800\) | \(1.3138\) | |
4830.g2 | 4830f1 | \([1, 1, 0, -5497, -158171]\) | \(18374873741826841/136564270080\) | \(136564270080\) | \([2]\) | \(6400\) | \(0.96720\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4830.g have rank \(1\).
Complex multiplication
The elliptic curves in class 4830.g do not have complex multiplication.Modular form 4830.2.a.g
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.