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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 183872.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 183872.bc1 | 183872t3 | \([0, 0, 0, -980876, 373911824]\) | \(82483294977/17\) | \(21510423314432\) | \([2]\) | \(1179648\) | \(1.9456\) | |
| 183872.bc2 | 183872t2 | \([0, 0, 0, -61516, 5800080]\) | \(20346417/289\) | \(365677196345344\) | \([2, 2]\) | \(589824\) | \(1.5990\) | |
| 183872.bc3 | 183872t1 | \([0, 0, 0, -7436, -105456]\) | \(35937/17\) | \(21510423314432\) | \([2]\) | \(294912\) | \(1.2524\) | \(\Gamma_0(N)\)-optimal |
| 183872.bc4 | 183872t4 | \([0, 0, 0, -7436, 15642640]\) | \(-35937/83521\) | \(-105680709743804416\) | \([2]\) | \(1179648\) | \(1.9456\) |
Rank
sage: E.rank()
The elliptic curves in class 183872.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 183872.bc do not have complex multiplication.Modular form 183872.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
