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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 377520.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.k1 | 377520k1 | \([0, -1, 0, -9178616, -174246071184]\) | \(-1426016903883782089/217897680469248000\) | \(-13067222793217064828928000\) | \([]\) | \(86220288\) | \(3.4987\) | \(\Gamma_0(N)\)-optimal |
| 377520.k2 | 377520k2 | \([0, -1, 0, 82558744, 4689155026800]\) | \(1037724929386537879751/158997676032000000000\) | \(-9535016856717361152000000000\) | \([]\) | \(258660864\) | \(4.0480\) |
Rank
sage: E.rank()
The elliptic curves in class 377520.k have rank \(0\).
Complex multiplication
The elliptic curves in class 377520.k do not have complex multiplication.Modular form 377520.2.a.k
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.
