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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 279312.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 279312.bl1 | 279312bl6 | \([0, -1, 0, -788032432, -8514337336832]\) | \(89254274298475942657/17457\) | \(10585139258462208\) | \([2]\) | \(34603008\) | \(3.3760\) | |
| 279312.bl2 | 279312bl4 | \([0, -1, 0, -49252192, -133023270080]\) | \(21790813729717297/304746849\) | \(184784776034974765056\) | \([2, 2]\) | \(17301504\) | \(3.0294\) | |
| 279312.bl3 | 279312bl5 | \([0, -1, 0, -47855632, -140923330688]\) | \(-19989223566735457/2584262514273\) | \(-1566980500315253734182912\) | \([2]\) | \(34603008\) | \(3.3760\) | |
| 279312.bl4 | 279312bl3 | \([0, -1, 0, -11925952, 13752037312]\) | \(309368403125137/44372288367\) | \(26905358972408640565248\) | \([4]\) | \(17301504\) | \(3.0294\) | |
| 279312.bl5 | 279312bl2 | \([0, -1, 0, -3165712, -1953320960]\) | \(5786435182177/627352209\) | \(380398149531356368896\) | \([2, 2]\) | \(8650752\) | \(2.6829\) | |
| 279312.bl6 | 279312bl1 | \([0, -1, 0, 262208, -151606208]\) | \(3288008303/18259263\) | \(-11071595440905449472\) | \([2]\) | \(4325376\) | \(2.3363\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 279312.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 279312.bl do not have complex multiplication.Modular form 279312.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
