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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 253920be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 253920.be3 | 253920be1 | \([0, -1, 0, -3350, 26352]\) | \(438976/225\) | \(2131716801600\) | \([2, 2]\) | \(394240\) | \(1.0579\) | \(\Gamma_0(N)\)-optimal |
| 253920.be1 | 253920be2 | \([0, -1, 0, -43025, 3446337]\) | \(14526784/15\) | \(9095325020160\) | \([2]\) | \(788480\) | \(1.4045\) | |
| 253920.be4 | 253920be3 | \([0, -1, 0, 12520, 191400]\) | \(2863288/1875\) | \(-142114453440000\) | \([2]\) | \(788480\) | \(1.4045\) | |
| 253920.be2 | 253920be4 | \([0, -1, 0, -29800, -1952108]\) | \(38614472/405\) | \(30696721943040\) | \([2]\) | \(788480\) | \(1.4045\) |
Rank
sage: E.rank()
The elliptic curves in class 253920be have rank \(1\).
Complex multiplication
The elliptic curves in class 253920be do not have complex multiplication.Modular form 253920.2.a.be
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.
