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SageMath
E = EllipticCurve("gv1")
E.isogeny_class()
Elliptic curves in class 430950gv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 430950.gv3 | 430950gv1 | \([1, 0, 0, -426813, 93685617]\) | \(114013572049/15667200\) | \(1181602843200000000\) | \([2]\) | \(10616832\) | \(2.1946\) | \(\Gamma_0(N)\)-optimal |
| 430950.gv2 | 430950gv2 | \([1, 0, 0, -1778813, -818914383]\) | \(8253429989329/936360000\) | \(70619232425625000000\) | \([2, 2]\) | \(21233664\) | \(2.5412\) | |
| 430950.gv4 | 430950gv3 | \([1, 0, 0, 2446187, -4118639383]\) | \(21464092074671/109596256200\) | \(-8265628059257278125000\) | \([2]\) | \(42467328\) | \(2.8877\) | |
| 430950.gv1 | 430950gv4 | \([1, 0, 0, -27635813, -55920181383]\) | \(30949975477232209/478125000\) | \(36059657080078125000\) | \([2]\) | \(42467328\) | \(2.8877\) |
Rank
sage: E.rank()
The elliptic curves in class 430950gv have rank \(1\).
Complex multiplication
The elliptic curves in class 430950gv do not have complex multiplication.Modular form 430950.2.a.gv
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.
