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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 69300bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69300.bl1 | 69300bm1 | \([0, 0, 0, -505200, -285941500]\) | \(-4890195460096/9282994875\) | \(-27069213055500000000\) | \([]\) | \(1492992\) | \(2.4185\) | \(\Gamma_0(N)\)-optimal |
| 69300.bl2 | 69300bm2 | \([0, 0, 0, 4354800, 6058788500]\) | \(3132137615458304/7250937873795\) | \(-21143734839986220000000\) | \([]\) | \(4478976\) | \(2.9678\) |
Rank
sage: E.rank()
The elliptic curves in class 69300bm have rank \(0\).
Complex multiplication
The elliptic curves in class 69300bm do not have complex multiplication.Modular form 69300.2.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.
