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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 243360bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 243360.bh3 | 243360bh1 | \([0, 0, 0, -9633, 123032]\) | \(438976/225\) | \(50669910158400\) | \([2, 2]\) | \(589824\) | \(1.3219\) | \(\Gamma_0(N)\)-optimal |
| 243360.bh1 | 243360bh2 | \([0, 0, 0, -123708, 16732352]\) | \(14526784/15\) | \(216191616675840\) | \([2]\) | \(1179648\) | \(1.6685\) | |
| 243360.bh4 | 243360bh3 | \([0, 0, 0, 35997, 953498]\) | \(2863288/1875\) | \(-3377994010560000\) | \([2]\) | \(1179648\) | \(1.6685\) | |
| 243360.bh2 | 243360bh4 | \([0, 0, 0, -85683, -9565738]\) | \(38614472/405\) | \(729646706280960\) | \([2]\) | \(1179648\) | \(1.6685\) |
Rank
sage: E.rank()
The elliptic curves in class 243360bh have rank \(0\).
Complex multiplication
The elliptic curves in class 243360bh do not have complex multiplication.Modular form 243360.2.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.
