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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 377520.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.bn1 | 377520bn2 | \([0, -1, 0, -5554076216, 159933967618416]\) | \(-21580315425730848803929/96405029296875000\) | \(-84644963134875000000000000000\) | \([]\) | \(615859200\) | \(4.4029\) | |
| 377520.bn2 | 377520bn1 | \([0, -1, 0, 164219224, 1160180075760]\) | \(557820238477845431/985142146218750\) | \(-864968573294139929472000000\) | \([]\) | \(205286400\) | \(3.8536\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 377520.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 377520.bn do not have complex multiplication.Modular form 377520.2.a.bn
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
