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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 72450.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72450.bj1 | 72450bu4 | \([1, -1, 0, -28269792, -32433123384]\) | \(219353215817909485369/87028564162480920\) | \(991309738663259229375000\) | \([2]\) | \(14155776\) | \(3.3028\) | |
| 72450.bj2 | 72450bu2 | \([1, -1, 0, -12834792, 17344751616]\) | \(20527812941011798969/474091398849600\) | \(5400197340021225000000\) | \([2, 2]\) | \(7077888\) | \(2.9562\) | |
| 72450.bj3 | 72450bu1 | \([1, -1, 0, -12762792, 17552759616]\) | \(20184279492242626489/11148103680\) | \(126983868480000000\) | \([2]\) | \(3538944\) | \(2.6096\) | \(\Gamma_0(N)\)-optimal |
| 72450.bj4 | 72450bu3 | \([1, -1, 0, 1448208, 53809250616]\) | \(29489595518609351/109830613939935000\) | \(-1251039336909572109375000\) | \([2]\) | \(14155776\) | \(3.3028\) |
Rank
sage: E.rank()
The elliptic curves in class 72450.bj have rank \(2\).
Complex multiplication
The elliptic curves in class 72450.bj do not have complex multiplication.Modular form 72450.2.a.bj
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.
