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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 418950i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 418950.i1 | 418950i1 | \([1, -1, 0, -19326963042, 1034178647895616]\) | \(595770186172725915913801/16492385700\) | \(22101374180076089062500\) | \([2]\) | \(454164480\) | \(4.2496\) | \(\Gamma_0(N)\)-optimal |
| 418950.i2 | 418950i2 | \([1, -1, 0, -19326191292, 1034265368671366]\) | \(-595698819458679957260521/99124922039928750\) | \(-132836875903001500060605468750\) | \([2]\) | \(908328960\) | \(4.5961\) |
Rank
sage: E.rank()
The elliptic curves in class 418950i have rank \(0\).
Complex multiplication
The elliptic curves in class 418950i do not have complex multiplication.Modular form 418950.2.a.i
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.
