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SageMath
E = EllipticCurve("er1")
E.isogeny_class()
Elliptic curves in class 224400er
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.bo2 | 224400er1 | \([0, -1, 0, -9115408, 58068133312]\) | \(-1308796492121439049/22000592486400000\) | \(-1408037919129600000000000\) | \([2]\) | \(28753920\) | \(3.3149\) | \(\Gamma_0(N)\)-optimal |
| 224400.bo1 | 224400er2 | \([0, -1, 0, -287643408, 1870728357312]\) | \(41125104693338423360329/179205840000000000\) | \(11469173760000000000000000\) | \([2]\) | \(57507840\) | \(3.6615\) |
Rank
sage: E.rank()
The elliptic curves in class 224400er have rank \(1\).
Complex multiplication
The elliptic curves in class 224400er do not have complex multiplication.Modular form 224400.2.a.er
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.
