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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 390g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 390.c4 | 390g1 | \([1, 0, 1, -289, 3092]\) | \(-2656166199049/2658140160\) | \(-2658140160\) | \([2]\) | \(320\) | \(0.50412\) | \(\Gamma_0(N)\)-optimal |
| 390.c3 | 390g2 | \([1, 0, 1, -5409, 152596]\) | \(17496824387403529/6580454400\) | \(6580454400\) | \([2, 2]\) | \(640\) | \(0.85069\) | |
| 390.c2 | 390g3 | \([1, 0, 1, -6209, 104276]\) | \(26465989780414729/10571870144160\) | \(10571870144160\) | \([2]\) | \(1280\) | \(1.1973\) | |
| 390.c1 | 390g4 | \([1, 0, 1, -86529, 9789652]\) | \(71647584155243142409/10140000\) | \(10140000\) | \([2]\) | \(1280\) | \(1.1973\) |
Rank
sage: E.rank()
The elliptic curves in class 390g have rank \(0\).
Complex multiplication
The elliptic curves in class 390g do not have complex multiplication.Modular form 390.2.a.g
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.
