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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2268.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2268.c1 | 2268c1 | \([0, 0, 0, -45, 117]\) | \(-864000/7\) | \(-81648\) | \([3]\) | \(216\) | \(-0.23004\) | \(\Gamma_0(N)\)-optimal |
| 2268.c2 | 2268c2 | \([0, 0, 0, 135, 621]\) | \(288000/343\) | \(-324060912\) | \([]\) | \(648\) | \(0.31927\) |
Rank
sage: E.rank()
The elliptic curves in class 2268.c have rank \(1\).
Complex multiplication
The elliptic curves in class 2268.c do not have complex multiplication.Modular form 2268.2.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.
