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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 23400.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23400.d1 | 23400l4 | \([0, 0, 0, -126360075, 546717437750]\) | \(19129597231400697604/26325\) | \(307054800000000\) | \([2]\) | \(1179648\) | \(2.9461\) | |
| 23400.d2 | 23400l2 | \([0, 0, 0, -7897575, 8542300250]\) | \(18681746265374416/693005625\) | \(2020804402500000000\) | \([2, 2]\) | \(589824\) | \(2.5996\) | |
| 23400.d3 | 23400l3 | \([0, 0, 0, -7533075, 9366434750]\) | \(-4053153720264484/903687890625\) | \(-10540615556250000000000\) | \([2]\) | \(1179648\) | \(2.9461\) | |
| 23400.d4 | 23400l1 | \([0, 0, 0, -516450, 120436625]\) | \(83587439220736/13990184325\) | \(2549711093231250000\) | \([2]\) | \(294912\) | \(2.2530\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23400.d have rank \(0\).
Complex multiplication
The elliptic curves in class 23400.d do not have complex multiplication.Modular form 23400.2.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.
