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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 229320bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.bp3 | 229320bl1 | \([0, 0, 0, -712125183, 7314466070338]\) | \(1819018058610682173904/4844385\) | \(106363932180629760\) | \([2]\) | \(33030144\) | \(3.3881\) | \(\Gamma_0(N)\)-optimal |
| 229320.bp2 | 229320bl2 | \([0, 0, 0, -712134003, 7314275824702]\) | \(454771411897393003396/23468066028225\) | \(2061071350387440399590400\) | \([2, 2]\) | \(66060288\) | \(3.7347\) | |
| 229320.bp4 | 229320bl3 | \([0, 0, 0, -673378923, 8145657551878]\) | \(-192245661431796830258/51935513760073125\) | \(-9122421877439685852360960000\) | \([2]\) | \(132120576\) | \(4.0813\) | |
| 229320.bp1 | 229320bl4 | \([0, 0, 0, -751030203, 6470718376822]\) | \(266716694084614489298/51372277695070605\) | \(9023490016954422501321123840\) | \([2]\) | \(132120576\) | \(4.0813\) |
Rank
sage: E.rank()
The elliptic curves in class 229320bl have rank \(1\).
Complex multiplication
The elliptic curves in class 229320bl do not have complex multiplication.Modular form 229320.2.a.bl
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.
