Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 37485bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37485.x2 | 37485bb1 | \([0, 0, 1, -62328, -7794761]\) | \(-312217698304/125355195\) | \(-10751228822348595\) | \([]\) | \(202752\) | \(1.7849\) | \(\Gamma_0(N)\)-optimal |
| 37485.x1 | 37485bb2 | \([0, 0, 1, -5460168, -4910855252]\) | \(-209906535145406464/6559875\) | \(-562615032994875\) | \([]\) | \(608256\) | \(2.3342\) |
Rank
sage: E.rank()
The elliptic curves in class 37485bb have rank \(0\).
Complex multiplication
The elliptic curves in class 37485bb do not have complex multiplication.Modular form 37485.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
