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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 98838.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98838.bh1 | 98838bl3 | \([1, -1, 1, -222440, 324868011]\) | \(-69173457625/2550136832\) | \(-44872941627802386432\) | \([]\) | \(2721600\) | \(2.4511\) | |
| 98838.bh2 | 98838bl1 | \([1, -1, 1, -40370, -3112887]\) | \(-413493625/152\) | \(-2674635745752\) | \([]\) | \(302400\) | \(1.3525\) | \(\Gamma_0(N)\)-optimal |
| 98838.bh3 | 98838bl2 | \([1, -1, 1, 24655, -11873055]\) | \(94196375/3511808\) | \(-61794784269854208\) | \([]\) | \(907200\) | \(1.9018\) |
Rank
sage: E.rank()
The elliptic curves in class 98838.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 98838.bh do not have complex multiplication.Modular form 98838.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
