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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 2100.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2100.e1 | 2100i2 | \([0, -1, 0, -1443708, -666974088]\) | \(665567485783184/257298363\) | \(128649181500000000\) | \([2]\) | \(40320\) | \(2.2484\) | |
| 2100.e2 | 2100i1 | \([0, -1, 0, -76833, -13607838]\) | \(-1605176213504/1640558367\) | \(-51267448968750000\) | \([2]\) | \(20160\) | \(1.9018\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2100.e have rank \(0\).
Complex multiplication
The elliptic curves in class 2100.e do not have complex multiplication.Modular form 2100.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
