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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1824.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1824.g1 | 1824i2 | \([0, 1, 0, -1824, -30600]\) | \(1311494070536/171\) | \(87552\) | \([2]\) | \(768\) | \(0.36359\) | |
1824.g2 | 1824i3 | \([0, 1, 0, -209, 351]\) | \(247673152/124659\) | \(510603264\) | \([4]\) | \(768\) | \(0.36359\) | |
1824.g3 | 1824i1 | \([0, 1, 0, -114, -504]\) | \(2582630848/29241\) | \(1871424\) | \([2, 2]\) | \(384\) | \(0.017017\) | \(\Gamma_0(N)\)-optimal |
1824.g4 | 1824i4 | \([0, 1, 0, -24, -1188]\) | \(-3112136/1172889\) | \(-600519168\) | \([2]\) | \(768\) | \(0.36359\) |
Rank
sage: E.rank()
The elliptic curves in class 1824.g have rank \(1\).
Complex multiplication
The elliptic curves in class 1824.g do not have complex multiplication.Modular form 1824.2.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.