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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 344760bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 344760.bm2 | 344760bm1 | \([0, 1, 0, 7549, 2935674]\) | \(615962624/48481875\) | \(-3744204009390000\) | \([2]\) | \(2064384\) | \(1.6678\) | \(\Gamma_0(N)\)-optimal |
| 344760.bm1 | 344760bm2 | \([0, 1, 0, -267076, 51159824]\) | \(1705021456336/68471325\) | \(84607489984492800\) | \([2]\) | \(4128768\) | \(2.0143\) |
Rank
sage: E.rank()
The elliptic curves in class 344760bm have rank \(2\).
Complex multiplication
The elliptic curves in class 344760bm do not have complex multiplication.Modular form 344760.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
