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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 408.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 408.d1 | 408b3 | \([0, 1, 0, -752, -8160]\) | \(22994537186/111537\) | \(228427776\) | \([2]\) | \(256\) | \(0.45230\) | |
| 408.d2 | 408b2 | \([0, 1, 0, -72, 0]\) | \(40873252/23409\) | \(23970816\) | \([2, 2]\) | \(128\) | \(0.10573\) | |
| 408.d3 | 408b1 | \([0, 1, 0, -52, 128]\) | \(61918288/153\) | \(39168\) | \([4]\) | \(64\) | \(-0.24084\) | \(\Gamma_0(N)\)-optimal |
| 408.d4 | 408b4 | \([0, 1, 0, 288, 288]\) | \(1285471294/751689\) | \(-1539459072\) | \([2]\) | \(256\) | \(0.45230\) |
Rank
sage: E.rank()
The elliptic curves in class 408.d have rank \(0\).
Complex multiplication
The elliptic curves in class 408.d do not have complex multiplication.Modular form 408.2.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.
