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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 35904.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35904.bh1 | 35904bx4 | \([0, -1, 0, -101523617, -393696369087]\) | \(441453577446719855661097/4354701912\) | \(1141558978019328\) | \([2]\) | \(2064384\) | \(2.9211\) | |
| 35904.bh2 | 35904bx2 | \([0, -1, 0, -6345377, -6149611455]\) | \(107784459654566688937/10704361149504\) | \(2806084049175576576\) | \([2, 2]\) | \(1032192\) | \(2.5745\) | |
| 35904.bh3 | 35904bx3 | \([0, -1, 0, -5866657, -7117104575]\) | \(-85183593440646799657/34223681512621656\) | \(-8971532766444691390464\) | \([2]\) | \(2064384\) | \(2.9211\) | |
| 35904.bh4 | 35904bx1 | \([0, -1, 0, -426657, -80555967]\) | \(32765849647039657/8229948198912\) | \(2157431540655587328\) | \([2]\) | \(516096\) | \(2.2279\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35904.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 35904.bh do not have complex multiplication.Modular form 35904.2.a.bh
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.
