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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 412224.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 412224.g1 | 412224g1 | \([0, -1, 0, -27891489, -56687097951]\) | \(9153747013124116391113/5485837418496\) | \(1438079364234215424\) | \([2]\) | \(20901888\) | \(2.8070\) | \(\Gamma_0(N)\)-optimal |
| 412224.g2 | 412224g2 | \([0, -1, 0, -27727649, -57386137695]\) | \(-8993380100968273380553/224220843480310272\) | \(-58778148793302455943168\) | \([2]\) | \(41803776\) | \(3.1536\) |
Rank
sage: E.rank()
The elliptic curves in class 412224.g have rank \(1\).
Complex multiplication
The elliptic curves in class 412224.g do not have complex multiplication.Modular form 412224.2.a.g
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.
