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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 119952.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 119952.bm1 | 119952ba1 | \([0, 0, 0, -4746, 123235]\) | \(2955053056/70227\) | \(280960810704\) | \([2]\) | \(143360\) | \(0.98187\) | \(\Gamma_0(N)\)-optimal |
| 119952.bm2 | 119952ba2 | \([0, 0, 0, 609, 385630]\) | \(390224/1003833\) | \(-64257390118656\) | \([2]\) | \(286720\) | \(1.3284\) |
Rank
sage: E.rank()
The elliptic curves in class 119952.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 119952.bm do not have complex multiplication.Modular form 119952.2.a.bm
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.
