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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 11154.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11154.w1 | 11154w3 | \([1, 1, 1, -844074, -298833969]\) | \(13778603383488553/13703976\) | \(66146474692584\) | \([2]\) | \(129024\) | \(1.9446\) | |
| 11154.w2 | 11154w4 | \([1, 1, 1, -127514, 11033615]\) | \(47504791830313/16490207448\) | \(79595081721873432\) | \([2]\) | \(129024\) | \(1.9446\) | |
| 11154.w3 | 11154w2 | \([1, 1, 1, -53154, -4611729]\) | \(3440899317673/106007616\) | \(511678514977344\) | \([2, 2]\) | \(64512\) | \(1.5980\) | |
| 11154.w4 | 11154w1 | \([1, 1, 1, 926, -242065]\) | \(18191447/5271552\) | \(-25444774637568\) | \([4]\) | \(32256\) | \(1.2515\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11154.w have rank \(0\).
Complex multiplication
The elliptic curves in class 11154.w do not have complex multiplication.Modular form 11154.2.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 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.
