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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 93600bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 93600.co3 | 93600bh1 | \([0, 0, 0, -14925, -654500]\) | \(504358336/38025\) | \(27720225000000\) | \([2, 2]\) | \(147456\) | \(1.3247\) | \(\Gamma_0(N)\)-optimal |
| 93600.co4 | 93600bh2 | \([0, 0, 0, 14325, -2906750]\) | \(55742968/658125\) | \(-3838185000000000\) | \([2]\) | \(294912\) | \(1.6712\) | |
| 93600.co2 | 93600bh3 | \([0, 0, 0, -48675, 3361750]\) | \(2186875592/428415\) | \(2498516280000000\) | \([4]\) | \(294912\) | \(1.6712\) | |
| 93600.co1 | 93600bh4 | \([0, 0, 0, -234300, -43652000]\) | \(30488290624/195\) | \(9097920000000\) | \([2]\) | \(294912\) | \(1.6712\) |
Rank
sage: E.rank()
The elliptic curves in class 93600bh have rank \(1\).
Complex multiplication
The elliptic curves in class 93600bh do not have complex multiplication.Modular form 93600.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
