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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 15030.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15030.d1 | 15030h3 | \([1, -1, 0, -19449, -945257]\) | \(1116093485689489/110938308750\) | \(80874027078750\) | \([2]\) | \(58368\) | \(1.4052\) | |
| 15030.d2 | 15030h2 | \([1, -1, 0, -4419, 97825]\) | \(13092526729009/2033108100\) | \(1482135804900\) | \([2, 2]\) | \(29184\) | \(1.0586\) | |
| 15030.d3 | 15030h1 | \([1, -1, 0, -4239, 107293]\) | \(11556972012529/360720\) | \(262964880\) | \([2]\) | \(14592\) | \(0.71205\) | \(\Gamma_0(N)\)-optimal |
| 15030.d4 | 15030h4 | \([1, -1, 0, 7731, 532795]\) | \(70092508729391/210005006670\) | \(-153093649862430\) | \([2]\) | \(58368\) | \(1.4052\) |
Rank
sage: E.rank()
The elliptic curves in class 15030.d have rank \(0\).
Complex multiplication
The elliptic curves in class 15030.d do not have complex multiplication.Modular form 15030.2.a.d
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 LMFDB 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 LMFDB labels.
