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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 110400dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 110400.hf4 | 110400dl1 | \([0, 1, 0, -395633, -613213137]\) | \(-26752376766544/618796614375\) | \(-158411933280000000000\) | \([2]\) | \(2359296\) | \(2.5567\) | \(\Gamma_0(N)\)-optimal |
| 110400.hf3 | 110400dl2 | \([0, 1, 0, -13517633, -19049623137]\) | \(266763091319403556/1355769140625\) | \(1388307600000000000000\) | \([2, 2]\) | \(4718592\) | \(2.9033\) | |
| 110400.hf2 | 110400dl3 | \([0, 1, 0, -20969633, 4282588863]\) | \(497927680189263938/284271240234375\) | \(582187500000000000000000\) | \([2]\) | \(9437184\) | \(3.2499\) | |
| 110400.hf1 | 110400dl4 | \([0, 1, 0, -216017633, -1222102123137]\) | \(544328872410114151778/14166950625\) | \(29013914880000000000\) | \([2]\) | \(9437184\) | \(3.2499\) |
Rank
sage: E.rank()
The elliptic curves in class 110400dl have rank \(1\).
Complex multiplication
The elliptic curves in class 110400dl do not have complex multiplication.Modular form 110400.2.a.dl
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.
