Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 340605.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
340605.c1 | 340605c2 | \([0, 0, 1, -90828, -10042171]\) | \(2359296/125\) | \(4390465285216125\) | \([]\) | \(1651104\) | \(1.7583\) | |
340605.c2 | 340605c1 | \([0, 0, 1, -15138, 713378]\) | \(884736/5\) | \(2168131005045\) | \([]\) | \(550368\) | \(1.2090\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 340605.c have rank \(1\).
Complex multiplication
The elliptic curves in class 340605.c do not have complex multiplication.Modular form 340605.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.