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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 4950.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4950.g1 | 4950o3 | \([1, -1, 0, -18117, 939541]\) | \(57736239625/255552\) | \(2910897000000\) | \([2]\) | \(13824\) | \(1.2439\) | |
4950.g2 | 4950o4 | \([1, -1, 0, -9117, 1866541]\) | \(-7357983625/127552392\) | \(-1452901465125000\) | \([2]\) | \(27648\) | \(1.5905\) | |
4950.g3 | 4950o1 | \([1, -1, 0, -1242, -15584]\) | \(18609625/1188\) | \(13532062500\) | \([2]\) | \(4608\) | \(0.69464\) | \(\Gamma_0(N)\)-optimal |
4950.g4 | 4950o2 | \([1, -1, 0, 1008, -67334]\) | \(9938375/176418\) | \(-2009511281250\) | \([2]\) | \(9216\) | \(1.0412\) |
Rank
sage: E.rank()
The elliptic curves in class 4950.g have rank \(1\).
Complex multiplication
The elliptic curves in class 4950.g do not have complex multiplication.Modular form 4950.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.