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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 1200.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1200.m1 | 1200q4 | \([0, 1, 0, -331208, -73238412]\) | \(502270291349/1889568\) | \(15116544000000000\) | \([2]\) | \(9600\) | \(1.9639\) | |
| 1200.m2 | 1200q2 | \([0, 1, 0, -21208, 1181588]\) | \(131872229/18\) | \(144000000000\) | \([2]\) | \(1920\) | \(1.1592\) | |
| 1200.m3 | 1200q3 | \([0, 1, 0, -11208, -2198412]\) | \(-19465109/248832\) | \(-1990656000000000\) | \([2]\) | \(4800\) | \(1.6173\) | |
| 1200.m4 | 1200q1 | \([0, 1, 0, -1208, 21588]\) | \(-24389/12\) | \(-96000000000\) | \([2]\) | \(960\) | \(0.81260\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1200.m have rank \(0\).
Complex multiplication
The elliptic curves in class 1200.m do not have complex multiplication.Modular form 1200.2.a.m
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.
