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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 138720bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
138720.o3 | 138720bl1 | \([0, -1, 0, -1830, 10800]\) | \(438976/225\) | \(347580993600\) | \([2, 2]\) | \(163840\) | \(0.90676\) | \(\Gamma_0(N)\)-optimal |
138720.o1 | 138720bl2 | \([0, -1, 0, -23505, 1393665]\) | \(14526784/15\) | \(1483012239360\) | \([2]\) | \(327680\) | \(1.2533\) | |
138720.o4 | 138720bl3 | \([0, -1, 0, 6840, 76692]\) | \(2863288/1875\) | \(-23172066240000\) | \([2]\) | \(327680\) | \(1.2533\) | |
138720.o2 | 138720bl4 | \([0, -1, 0, -16280, -786840]\) | \(38614472/405\) | \(5005166307840\) | \([2]\) | \(327680\) | \(1.2533\) |
Rank
sage: E.rank()
The elliptic curves in class 138720bl have rank \(0\).
Complex multiplication
The elliptic curves in class 138720bl do not have complex multiplication.Modular form 138720.2.a.bl
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.