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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 5390.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5390.bj1 | 5390bf4 | \([1, 1, 1, -1279685, 540867487]\) | \(1969902499564819009/63690429687500\) | \(7493115362304687500\) | \([2]\) | \(165888\) | \(2.3956\) | |
| 5390.bj2 | 5390bf2 | \([1, 1, 1, -175225, -28054265]\) | \(5057359576472449/51765560000\) | \(6090166368440000\) | \([2]\) | \(55296\) | \(1.8463\) | |
| 5390.bj3 | 5390bf1 | \([1, 1, 1, -2745, -1078393]\) | \(-19443408769/4249907200\) | \(-499997332172800\) | \([2]\) | \(27648\) | \(1.4997\) | \(\Gamma_0(N)\)-optimal |
| 5390.bj4 | 5390bf3 | \([1, 1, 1, 24695, 29028775]\) | \(14156681599871/3100231750000\) | \(-364739165155750000\) | \([2]\) | \(82944\) | \(2.0490\) |
Rank
sage: E.rank()
The elliptic curves in class 5390.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 5390.bj do not have complex multiplication.Modular form 5390.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
