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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 109005.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 109005.c1 | 109005g4 | \([1, 1, 1, -116360, 15229040]\) | \(36097320816649/80625\) | \(389161475625\) | \([2]\) | \(337920\) | \(1.4691\) | |
| 109005.c2 | 109005g3 | \([1, 1, 1, -20030, -794188]\) | \(184122897769/51282015\) | \(247528491540135\) | \([2]\) | \(337920\) | \(1.4691\) | |
| 109005.c3 | 109005g2 | \([1, 1, 1, -7355, 229952]\) | \(9116230969/416025\) | \(2008073214225\) | \([2, 2]\) | \(168960\) | \(1.1225\) | |
| 109005.c4 | 109005g1 | \([1, 1, 1, 250, 13970]\) | \(357911/17415\) | \(-84058878735\) | \([2]\) | \(84480\) | \(0.77597\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 109005.c have rank \(1\).
Complex multiplication
The elliptic curves in class 109005.c do not have complex multiplication.Modular form 109005.2.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.
