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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 6720.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6720.bh1 | 6720r3 | \([0, 1, 0, -336001, -75077185]\) | \(128025588102048008/7875\) | \(258048000\) | \([2]\) | \(24576\) | \(1.5225\) | |
| 6720.bh2 | 6720r4 | \([0, 1, 0, -23521, -880321]\) | \(43919722445768/15380859375\) | \(504000000000000\) | \([2]\) | \(24576\) | \(1.5225\) | |
| 6720.bh3 | 6720r2 | \([0, 1, 0, -21001, -1178185]\) | \(250094631024064/62015625\) | \(254016000000\) | \([2, 2]\) | \(12288\) | \(1.1760\) | |
| 6720.bh4 | 6720r1 | \([0, 1, 0, -1156, -23206]\) | \(-2671731885376/1969120125\) | \(-126023688000\) | \([2]\) | \(6144\) | \(0.82939\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6720.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 6720.bh do not have complex multiplication.Modular form 6720.2.a.bh
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
