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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 64400.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64400.bl1 | 64400bo4 | \([0, 0, 0, -49475, -4234750]\) | \(209267191953/55223\) | \(3534272000000\) | \([2]\) | \(163840\) | \(1.3922\) | |
| 64400.bl2 | 64400bo2 | \([0, 0, 0, -3475, -48750]\) | \(72511713/25921\) | \(1658944000000\) | \([2, 2]\) | \(81920\) | \(1.0457\) | |
| 64400.bl3 | 64400bo1 | \([0, 0, 0, -1475, 21250]\) | \(5545233/161\) | \(10304000000\) | \([2]\) | \(40960\) | \(0.69909\) | \(\Gamma_0(N)\)-optimal |
| 64400.bl4 | 64400bo3 | \([0, 0, 0, 10525, -342750]\) | \(2014698447/1958887\) | \(-125368768000000\) | \([2]\) | \(163840\) | \(1.3922\) |
Rank
sage: E.rank()
The elliptic curves in class 64400.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 64400.bl do not have complex multiplication.Modular form 64400.2.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 LMFDB 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 LMFDB labels.
