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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 107800.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107800.bc1 | 107800bo2 | \([0, 0, 0, -434875, -30098250]\) | \(2415899250/1294139\) | \(4872133094752000000\) | \([2]\) | \(1327104\) | \(2.2771\) | |
| 107800.bc2 | 107800bo1 | \([0, 0, 0, 104125, -3687250]\) | \(66325500/41503\) | \(-78124583152000000\) | \([2]\) | \(663552\) | \(1.9305\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 107800.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 107800.bc do not have complex multiplication.Modular form 107800.2.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.
