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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 19074.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19074.bc1 | 19074bb2 | \([1, 0, 0, -320242929, 1572341194089]\) | \(150476552140919246594353/42832838728685592576\) | \(1033880600279520770109087744\) | \([2]\) | \(9345024\) | \(3.8903\) | |
| 19074.bc2 | 19074bb1 | \([1, 0, 0, -119006449, -480311149207]\) | \(7722211175253055152433/340131399900069888\) | \(8209945134154530026422272\) | \([2]\) | \(4672512\) | \(3.5437\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19074.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 19074.bc do not have complex multiplication.Modular form 19074.2.a.bc
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
