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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 24150.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24150.bd1 | 24150x4 | \([1, 0, 1, -923002501, 10792793669648]\) | \(5565604209893236690185614401/229307220930246900000\) | \(3582925327035107812500000\) | \([2]\) | \(14745600\) | \(3.7929\) | |
| 24150.bd2 | 24150x3 | \([1, 0, 1, -281394501, -1675508170352]\) | \(157706830105239346386477121/13650704956054687500000\) | \(213292264938354492187500000\) | \([2]\) | \(14745600\) | \(3.7929\) | |
| 24150.bd3 | 24150x2 | \([1, 0, 1, -60502501, 151268669648]\) | \(1567558142704512417614401/274462175610000000000\) | \(4288471493906250000000000\) | \([2, 2]\) | \(7372800\) | \(3.4463\) | |
| 24150.bd4 | 24150x1 | \([1, 0, 1, 7209499, 13542461648]\) | \(2652277923951208297919/6605028468326400000\) | \(-103203569817600000000000\) | \([2]\) | \(3686400\) | \(3.0998\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24150.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 24150.bd do not have complex multiplication.Modular form 24150.2.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.
