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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 145794w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145794.r3 | 145794w1 | \([1, 0, 1, -12196, -489970]\) | \(18609625/1188\) | \(12805707810852\) | \([2]\) | \(417312\) | \(1.2657\) | \(\Gamma_0(N)\)-optimal |
| 145794.r4 | 145794w2 | \([1, 0, 1, 9894, -2062778]\) | \(9938375/176418\) | \(-1901647609911522\) | \([2]\) | \(834624\) | \(1.6123\) | |
| 145794.r1 | 145794w3 | \([1, 0, 1, -177871, 28748354]\) | \(57736239625/255552\) | \(2754650035756608\) | \([2]\) | \(1251936\) | \(1.8150\) | |
| 145794.r2 | 145794w4 | \([1, 0, 1, -89511, 57341650]\) | \(-7357983625/127552392\) | \(-1374914699097016968\) | \([2]\) | \(2503872\) | \(2.1616\) |
Rank
sage: E.rank()
The elliptic curves in class 145794w have rank \(0\).
Complex multiplication
The elliptic curves in class 145794w do not have complex multiplication.Modular form 145794.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
