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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 173400.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 173400.c1 | 173400ef3 | \([0, -1, 0, -707474408, 7243164616812]\) | \(50700519510140162/2295\) | \(1772663067360000000\) | \([2]\) | \(31850496\) | \(3.4306\) | |
| 173400.c2 | 173400ef4 | \([0, -1, 0, -49132408, 86476124812]\) | \(16981825082402/5646560625\) | \(4361415894355860000000000\) | \([2]\) | \(31850496\) | \(3.4306\) | |
| 173400.c3 | 173400ef2 | \([0, -1, 0, -44219408, 113173366812]\) | \(24759905519524/5267025\) | \(2034130869795600000000\) | \([2, 2]\) | \(15925248\) | \(3.0840\) | |
| 173400.c4 | 173400ef1 | \([0, -1, 0, -2458908, 2173957812]\) | \(-17029316176/11275335\) | \(-1088636706242460000000\) | \([2]\) | \(7962624\) | \(2.7375\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 173400.c have rank \(1\).
Complex multiplication
The elliptic curves in class 173400.c do not have complex multiplication.Modular form 173400.2.a.c
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.
