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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 303240.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 303240.bl1 | 303240bl3 | \([0, 1, 0, -1348816, 602493584]\) | \(5633270409316/14175\) | \(682880371891200\) | \([2]\) | \(3538944\) | \(2.0847\) | |
| 303240.bl2 | 303240bl4 | \([0, 1, 0, -236936, -32571840]\) | \(30534944836/8203125\) | \(395185400400000000\) | \([2]\) | \(3538944\) | \(2.0847\) | |
| 303240.bl3 | 303240bl2 | \([0, 1, 0, -85316, 9153984]\) | \(5702413264/275625\) | \(3319557363360000\) | \([2, 2]\) | \(1769472\) | \(1.7381\) | |
| 303240.bl4 | 303240bl1 | \([0, 1, 0, 3129, 557130]\) | \(4499456/180075\) | \(-135548592337200\) | \([2]\) | \(884736\) | \(1.3915\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303240.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 303240.bl do not have complex multiplication.Modular form 303240.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
