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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 2400r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2400.j3 | 2400r1 | \([0, -1, 0, -158, 312]\) | \(438976/225\) | \(225000000\) | \([2, 2]\) | \(768\) | \(0.29488\) | \(\Gamma_0(N)\)-optimal |
| 2400.j2 | 2400r2 | \([0, -1, 0, -1408, -19688]\) | \(38614472/405\) | \(3240000000\) | \([2]\) | \(1536\) | \(0.64145\) | |
| 2400.j1 | 2400r3 | \([0, -1, 0, -2033, 35937]\) | \(14526784/15\) | \(960000000\) | \([4]\) | \(1536\) | \(0.64145\) | |
| 2400.j4 | 2400r4 | \([0, -1, 0, 592, 1812]\) | \(2863288/1875\) | \(-15000000000\) | \([2]\) | \(1536\) | \(0.64145\) |
Rank
sage: E.rank()
The elliptic curves in class 2400r have rank \(0\).
Complex multiplication
The elliptic curves in class 2400r 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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
