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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 20328bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20328.j2 | 20328bd1 | \([0, 1, 0, -406600, 118930304]\) | \(-4097989445764/1004475087\) | \(-1822196622951226368\) | \([2]\) | \(460800\) | \(2.2222\) | \(\Gamma_0(N)\)-optimal |
| 20328.j1 | 20328bd2 | \([0, 1, 0, -6848640, 6895956384]\) | \(9791533777258802/427901859\) | \(1552495094234929152\) | \([2]\) | \(921600\) | \(2.5687\) |
Rank
sage: E.rank()
The elliptic curves in class 20328bd have rank \(1\).
Complex multiplication
The elliptic curves in class 20328bd do not have complex multiplication.Modular form 20328.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
