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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 180336.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 180336.bd1 | 180336da4 | \([0, -1, 0, -4087712, -3179673552]\) | \(305612563186948/663\) | \(16387285244928\) | \([2]\) | \(3538944\) | \(2.2095\) | |
| 180336.bd2 | 180336da3 | \([0, -1, 0, -330712, -17962688]\) | \(161838334948/87947613\) | \(2173789775024944128\) | \([2]\) | \(3538944\) | \(2.2095\) | |
| 180336.bd3 | 180336da2 | \([0, -1, 0, -255572, -49581600]\) | \(298766385232/439569\) | \(2716192529346816\) | \([2, 2]\) | \(1769472\) | \(1.8629\) | |
| 180336.bd4 | 180336da1 | \([0, -1, 0, -11367, -1229010]\) | \(-420616192/1456611\) | \(-562544776298544\) | \([2]\) | \(884736\) | \(1.5163\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 180336.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 180336.bd do not have complex multiplication.Modular form 180336.2.a.bd
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.
