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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 309738.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 309738.bd1 | 309738bd3 | \([1, 0, 1, -4789395, 4007663686]\) | \(258252149810350513/1938176193096\) | \(91183206537427437576\) | \([2]\) | \(15925248\) | \(2.6601\) | |
| 309738.bd2 | 309738bd2 | \([1, 0, 1, -500715, -32272874]\) | \(295102348042033/161237583936\) | \(7585564186580567616\) | \([2, 2]\) | \(7962624\) | \(2.3135\) | |
| 309738.bd3 | 309738bd1 | \([1, 0, 1, -385195, -91927402]\) | \(134351465835313/205590528\) | \(9672187515015168\) | \([2]\) | \(3981312\) | \(1.9669\) | \(\Gamma_0(N)\)-optimal |
| 309738.bd4 | 309738bd4 | \([1, 0, 1, 1939645, -253857562]\) | \(17154149157653327/10519679024712\) | \(-494907567554796811272\) | \([2]\) | \(15925248\) | \(2.6601\) |
Rank
sage: E.rank()
The elliptic curves in class 309738.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 309738.bd do not have complex multiplication.Modular form 309738.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
