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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1200.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1200.g1 | 1200m4 | \([0, -1, 0, -13248, -580608]\) | \(502270291349/1889568\) | \(967458816000\) | \([2]\) | \(1920\) | \(1.1592\) | |
| 1200.g2 | 1200m2 | \([0, -1, 0, -848, 9792]\) | \(131872229/18\) | \(9216000\) | \([2]\) | \(384\) | \(0.35445\) | |
| 1200.g3 | 1200m3 | \([0, -1, 0, -448, -17408]\) | \(-19465109/248832\) | \(-127401984000\) | \([2]\) | \(960\) | \(0.81260\) | |
| 1200.g4 | 1200m1 | \([0, -1, 0, -48, 192]\) | \(-24389/12\) | \(-6144000\) | \([2]\) | \(192\) | \(0.0078760\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1200.g have rank \(1\).
Complex multiplication
The elliptic curves in class 1200.g do not have complex multiplication.Modular form 1200.2.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.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
