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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 173400bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 173400.d1 | 173400bf1 | \([0, -1, 0, -58835583, 173704965912]\) | \(29860725364736/3581577\) | \(2701580061447281250000\) | \([2]\) | \(21565440\) | \(3.1371\) | \(\Gamma_0(N)\)-optimal |
| 173400.d2 | 173400bf2 | \([0, -1, 0, -53958708, 203687993412]\) | \(-1439609866256/651714363\) | \(-7865400202601773500000000\) | \([2]\) | \(43130880\) | \(3.4837\) |
Rank
sage: E.rank()
The elliptic curves in class 173400bf have rank \(1\).
Complex multiplication
The elliptic curves in class 173400bf do not have complex multiplication.Modular form 173400.2.a.bf
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
