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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 24255bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24255.bl3 | 24255bh1 | \([1, -1, 0, -4860, -102789]\) | \(148035889/31185\) | \(2674616483385\) | \([2]\) | \(36864\) | \(1.0993\) | \(\Gamma_0(N)\)-optimal |
| 24255.bl2 | 24255bh2 | \([1, -1, 0, -24705, 1409400]\) | \(19443408769/1334025\) | \(114414149567025\) | \([2, 2]\) | \(73728\) | \(1.4458\) | |
| 24255.bl4 | 24255bh3 | \([1, -1, 0, 21600, 6049161]\) | \(12994449551/192163125\) | \(-16481085830488125\) | \([2]\) | \(147456\) | \(1.7924\) | |
| 24255.bl1 | 24255bh4 | \([1, -1, 0, -388530, 93311595]\) | \(75627935783569/396165\) | \(33977535325965\) | \([2]\) | \(147456\) | \(1.7924\) |
Rank
sage: E.rank()
The elliptic curves in class 24255bh have rank \(0\).
Complex multiplication
The elliptic curves in class 24255bh do not have complex multiplication.Modular form 24255.2.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 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.
