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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 30030h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30030.h4 | 30030h1 | \([1, 1, 0, 63973, -234793059]\) | \(28953645767800656839/23837364409098240000\) | \(-23837364409098240000\) | \([2]\) | \(1032192\) | \(2.3972\) | \(\Gamma_0(N)\)-optimal |
| 30030.h3 | 30030h2 | \([1, 1, 0, -5344027, -4646639459]\) | \(16878341517236150848175161/449072473950125625600\) | \(449072473950125625600\) | \([2, 2]\) | \(2064384\) | \(2.7437\) | |
| 30030.h2 | 30030h3 | \([1, 1, 0, -12265227, 9861579981]\) | \(204056549450239798253019961/76032397822040370350640\) | \(76032397822040370350640\) | \([2]\) | \(4128768\) | \(3.0903\) | |
| 30030.h1 | 30030h4 | \([1, 1, 0, -84950827, -301404868499]\) | \(67799509729837845667504002361/49968048019990660560\) | \(49968048019990660560\) | \([2]\) | \(4128768\) | \(3.0903\) |
Rank
sage: E.rank()
The elliptic curves in class 30030h have rank \(0\).
Complex multiplication
The elliptic curves in class 30030h do not have complex multiplication.Modular form 30030.2.a.h
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.
