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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 88935.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88935.bz1 | 88935cg4 | \([1, 0, 1, -5223573, 4594692463]\) | \(75627935783569/396165\) | \(82569652207958685\) | \([2]\) | \(2211840\) | \(2.4420\) | |
| 88935.bz2 | 88935cg2 | \([1, 0, 1, -332148, 69146053]\) | \(19443408769/1334025\) | \(278040665598228225\) | \([2, 2]\) | \(1105920\) | \(2.0955\) | |
| 88935.bz3 | 88935cg1 | \([1, 0, 1, -65343, -5132459]\) | \(148035889/31185\) | \(6499651923075465\) | \([2]\) | \(552960\) | \(1.7489\) | \(\Gamma_0(N)\)-optimal |
| 88935.bz4 | 88935cg3 | \([1, 0, 1, 290397, 298491631]\) | \(12994449551/192163125\) | \(-40051095877840018125\) | \([2]\) | \(2211840\) | \(2.4420\) |
Rank
sage: E.rank()
The elliptic curves in class 88935.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 88935.bz do not have complex multiplication.Modular form 88935.2.a.bz
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.
