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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 70560.db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70560.db1 | 70560du4 | \([0, 0, 0, -6227067, 5980987726]\) | \(608119035935048/826875\) | \(36309944986560000\) | \([2]\) | \(1179648\) | \(2.4518\) | |
| 70560.db2 | 70560du3 | \([0, 0, 0, -987987, -252517286]\) | \(2428799546888/778248135\) | \(34174629741790379520\) | \([2]\) | \(1179648\) | \(2.4518\) | |
| 70560.db3 | 70560du1 | \([0, 0, 0, -392637, 91714084]\) | \(1219555693504/43758225\) | \(240190286086094400\) | \([2, 2]\) | \(589824\) | \(2.1052\) | \(\Gamma_0(N)\)-optimal |
| 70560.db4 | 70560du2 | \([0, 0, 0, 147588, 324659104]\) | \(1012048064/130203045\) | \(-45740073418909470720\) | \([2]\) | \(1179648\) | \(2.4518\) |
Rank
sage: E.rank()
The elliptic curves in class 70560.db have rank \(1\).
Complex multiplication
The elliptic curves in class 70560.db do not have complex multiplication.Modular form 70560.2.a.db
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
