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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 427856i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 427856.i1 | 427856i1 | \([0, 1, 0, -115232, 15015988]\) | \(23320116793/2873\) | \(20847389708288\) | \([2]\) | \(1658880\) | \(1.5791\) | \(\Gamma_0(N)\)-optimal |
| 427856.i2 | 427856i2 | \([0, 1, 0, -105552, 17652820]\) | \(-17923019113/8254129\) | \(-59894550631911424\) | \([2]\) | \(3317760\) | \(1.9256\) |
Rank
sage: E.rank()
The elliptic curves in class 427856i have rank \(0\).
Complex multiplication
The elliptic curves in class 427856i do not have complex multiplication.Modular form 427856.2.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.
