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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 960.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
960.g1 | 960c3 | \([0, -1, 0, -865, -9503]\) | \(546718898/405\) | \(53084160\) | \([2]\) | \(512\) | \(0.41598\) | |
960.g2 | 960c4 | \([0, -1, 0, -545, 5025]\) | \(136835858/1875\) | \(245760000\) | \([4]\) | \(512\) | \(0.41598\) | |
960.g3 | 960c2 | \([0, -1, 0, -65, -63]\) | \(470596/225\) | \(14745600\) | \([2, 2]\) | \(256\) | \(0.069403\) | |
960.g4 | 960c1 | \([0, -1, 0, 15, -15]\) | \(21296/15\) | \(-245760\) | \([2]\) | \(128\) | \(-0.27717\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 960.g have rank \(0\).
Complex multiplication
The elliptic curves in class 960.g do not have complex multiplication.Modular form 960.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.