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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 40460.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40460.c1 | 40460q2 | \([0, 1, 0, -55299090, -889776298187]\) | \(-167558444566341376/2967225943714375\) | \(-331178375295900777358630000\) | \([]\) | \(15202080\) | \(3.7699\) | |
40460.c2 | 40460q1 | \([0, 1, 0, 6113410, 32037609313]\) | \(226392928058624/4103271484375\) | \(-457974825433152343750000\) | \([3]\) | \(5067360\) | \(3.2205\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40460.c have rank \(1\).
Complex multiplication
The elliptic curves in class 40460.c do not have complex multiplication.Modular form 40460.2.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.