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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 48510bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48510.w3 | 48510bb1 | \([1, -1, 0, -24705, 29091901]\) | \(-19443408769/4249907200\) | \(-364498055153971200\) | \([2]\) | \(663552\) | \(2.0490\) | \(\Gamma_0(N)\)-optimal |
| 48510.w2 | 48510bb2 | \([1, -1, 0, -1577025, 755888125]\) | \(5057359576472449/51765560000\) | \(4439731282592760000\) | \([2]\) | \(1327104\) | \(2.3956\) | |
| 48510.w4 | 48510bb3 | \([1, -1, 0, 222255, -783554675]\) | \(14156681599871/3100231750000\) | \(-265894851398541750000\) | \([2]\) | \(1990656\) | \(2.5984\) | |
| 48510.w1 | 48510bb4 | \([1, -1, 0, -11517165, -14614939319]\) | \(1969902499564819009/63690429687500\) | \(5462481099120117187500\) | \([2]\) | \(3981312\) | \(2.9449\) |
Rank
sage: E.rank()
The elliptic curves in class 48510bb have rank \(0\).
Complex multiplication
The elliptic curves in class 48510bb do not have complex multiplication.Modular form 48510.2.a.bb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
