Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 70602a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
70602.b2 | 70602a1 | \([1, 1, 0, -2915565, 1914947613]\) | \(1630513562870774583625/3950456832\) | \(6640717934592\) | \([]\) | \(1233792\) | \(2.1271\) | \(\Gamma_0(N)\)-optimal |
70602.b1 | 70602a2 | \([1, 1, 0, -3009660, 1784623824]\) | \(1793529535985843517625/218288998399868928\) | \(366943806310179667968\) | \([]\) | \(3701376\) | \(2.6764\) |
Rank
sage: E.rank()
The elliptic curves in class 70602a have rank \(1\).
Complex multiplication
The elliptic curves in class 70602a do not have complex multiplication.Modular form 70602.2.a.a
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 Cremona 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 Cremona labels.