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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 53312bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53312.h1 | 53312bk1 | \([0, 1, 0, -14177, -740321]\) | \(-208537/34\) | \(-51381071773696\) | \([]\) | \(161280\) | \(1.3584\) | \(\Gamma_0(N)\)-optimal |
| 53312.h2 | 53312bk2 | \([0, 1, 0, 95583, 2881759]\) | \(63905303/39304\) | \(-59396518970392576\) | \([]\) | \(483840\) | \(1.9077\) |
Rank
sage: E.rank()
The elliptic curves in class 53312bk have rank \(0\).
Complex multiplication
The elliptic curves in class 53312bk do not have complex multiplication.Modular form 53312.2.a.bk
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.
