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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 24990a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24990.e3 | 24990a1 | \([1, 1, 0, -2513333, -1534672467]\) | \(14924020698027934921/161083883520\) | \(18951357812244480\) | \([2]\) | \(737280\) | \(2.2785\) | \(\Gamma_0(N)\)-optimal |
| 24990.e2 | 24990a2 | \([1, 1, 0, -2576053, -1454127443]\) | \(16069416876629693641/1546622367494400\) | \(181958574913348665600\) | \([2, 2]\) | \(1474560\) | \(2.6251\) | |
| 24990.e4 | 24990a3 | \([1, 1, 0, 3088347, -6951994083]\) | \(27689398696638536759/193555307298039120\) | \(-22771588348307004428880\) | \([2]\) | \(2949120\) | \(2.9716\) | |
| 24990.e1 | 24990a4 | \([1, 1, 0, -9243973, 9199875133]\) | \(742525803457216841161/118657634071410000\) | \(13959951990867315090000\) | \([2]\) | \(2949120\) | \(2.9716\) |
Rank
sage: E.rank()
The elliptic curves in class 24990a have rank \(0\).
Complex multiplication
The elliptic curves in class 24990a do not have complex multiplication.Modular form 24990.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
