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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 135240.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 135240.bv1 | 135240bk1 | \([0, -1, 0, -112474420, -459080086268]\) | \(5224645130090610708304/67370009765625\) | \(2029059655402500000000\) | \([2]\) | \(20643840\) | \(3.2336\) | \(\Gamma_0(N)\)-optimal |
| 135240.bv2 | 135240bk2 | \([0, -1, 0, -109411920, -485262011268]\) | \(-1202345928696155427076/148724718496003125\) | \(-17917249952088342172800000\) | \([2]\) | \(41287680\) | \(3.5802\) |
Rank
sage: E.rank()
The elliptic curves in class 135240.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 135240.bv do not have complex multiplication.Modular form 135240.2.a.bv
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.
