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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 301530be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 301530.be4 | 301530be1 | \([1, 0, 1, 1944857, 6265681898]\) | \(5495662324535111/117739817533440\) | \(-17429718559260577628160\) | \([2]\) | \(28385280\) | \(2.9480\) | \(\Gamma_0(N)\)-optimal |
| 301530.be3 | 301530be2 | \([1, 0, 1, -41390823, 97079932906]\) | \(52974743974734147769/3152005008998400\) | \(466609863639531143577600\) | \([2, 2]\) | \(56770560\) | \(3.2946\) | |
| 301530.be1 | 301530be3 | \([1, 0, 1, -652491623, 6415128883946]\) | \(207530301091125281552569/805586668007040\) | \(119255738564970024658560\) | \([2]\) | \(113541120\) | \(3.6412\) | |
| 301530.be2 | 301530be4 | \([1, 0, 1, -123660903, -408683610902]\) | \(1412712966892699019449/330160465517040000\) | \(48875598025468861048560000\) | \([2]\) | \(113541120\) | \(3.6412\) |
Rank
sage: E.rank()
The elliptic curves in class 301530be have rank \(1\).
Complex multiplication
The elliptic curves in class 301530be do not have complex multiplication.Modular form 301530.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
