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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 297825bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 297825.bm1 | 297825bm1 | \([0, 1, 1, -8423, -314956]\) | \(-56197120/3267\) | \(-3842472330675\) | \([]\) | \(454896\) | \(1.1710\) | \(\Gamma_0(N)\)-optimal |
| 297825.bm2 | 297825bm2 | \([0, 1, 1, 45727, -536971]\) | \(8990228480/5314683\) | \(-6250848599268075\) | \([]\) | \(1364688\) | \(1.7203\) |
Rank
sage: E.rank()
The elliptic curves in class 297825bm have rank \(1\).
Complex multiplication
The elliptic curves in class 297825bm do not have complex multiplication.Modular form 297825.2.a.bm
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.
