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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 428400w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 428400.w2 | 428400w1 | \([0, 0, 0, -12903435, 17839697850]\) | \(23576453352214407/1170305024\) | \(11793978259144704000\) | \([2]\) | \(22118400\) | \(2.7309\) | \(\Gamma_0(N)\)-optimal |
| 428400.w1 | 428400w2 | \([0, 0, 0, -13594635, 15822085050]\) | \(27571799648846727/5224662205504\) | \(52652557409758838784000\) | \([2]\) | \(44236800\) | \(3.0774\) |
Rank
sage: E.rank()
The elliptic curves in class 428400w have rank \(0\).
Complex multiplication
The elliptic curves in class 428400w do not have complex multiplication.Modular form 428400.2.a.w
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.
