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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 166635.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166635.bl1 | 166635bx1 | \([1, -1, 0, -2194920, 1220525075]\) | \(292583028222603/8456021875\) | \(33798457323064940625\) | \([2]\) | \(4561920\) | \(2.5252\) | \(\Gamma_0(N)\)-optimal |
166635.bl2 | 166635bx2 | \([1, -1, 0, 526785, 4046199206]\) | \(4044759171237/1771943359375\) | \(-7082402682493564453125\) | \([2]\) | \(9123840\) | \(2.8718\) |
Rank
sage: E.rank()
The elliptic curves in class 166635.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 166635.bl do not have complex multiplication.Modular form 166635.2.a.bl
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.