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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 2400.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2400.r1 | 2400m2 | \([0, 1, 0, -808, -9112]\) | \(7301384/3\) | \(24000000\) | \([2]\) | \(1024\) | \(0.37850\) | |
2400.r2 | 2400m3 | \([0, 1, 0, -433, 3263]\) | \(140608/3\) | \(192000000\) | \([2]\) | \(1024\) | \(0.37850\) | |
2400.r3 | 2400m1 | \([0, 1, 0, -58, -112]\) | \(21952/9\) | \(9000000\) | \([2, 2]\) | \(512\) | \(0.031925\) | \(\Gamma_0(N)\)-optimal |
2400.r4 | 2400m4 | \([0, 1, 0, 192, -612]\) | \(97336/81\) | \(-648000000\) | \([2]\) | \(1024\) | \(0.37850\) |
Rank
sage: E.rank()
The elliptic curves in class 2400.r have rank \(0\).
Complex multiplication
The elliptic curves in class 2400.r do not have complex multiplication.Modular form 2400.2.a.r
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.