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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 50715.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50715.bm1 | 50715b1 | \([1, -1, 0, -203310, 34443191]\) | \(292583028222603/8456021875\) | \(26860747974440625\) | \([2]\) | \(414720\) | \(1.9304\) | \(\Gamma_0(N)\)-optimal |
| 50715.bm2 | 50715b2 | \([1, -1, 0, 48795, 114057950]\) | \(4044759171237/1771943359375\) | \(-5628618835751953125\) | \([2]\) | \(829440\) | \(2.2770\) |
Rank
sage: E.rank()
The elliptic curves in class 50715.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 50715.bm do not have complex multiplication.Modular form 50715.2.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 LMFDB 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 LMFDB labels.
