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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 170352.ev
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 170352.ev1 | 170352ci3 | \([0, 0, 0, -328950219, 2295553874042]\) | \(124318741396429/51631104\) | \(1634891961493799282147328\) | \([2]\) | \(29952000\) | \(3.6080\) | |
| 170352.ev2 | 170352ci4 | \([0, 0, 0, -278331339, 3026115921530]\) | \(-75306487574989/81352871712\) | \(-2576027737202464175160950784\) | \([2]\) | \(59904000\) | \(3.9545\) | |
| 170352.ev3 | 170352ci1 | \([0, 0, 0, -11000379, -14025221782]\) | \(4649101309/6804\) | \(215447744561181769728\) | \([2]\) | \(5990400\) | \(2.8033\) | \(\Gamma_0(N)\)-optimal |
| 170352.ev4 | 170352ci2 | \([0, 0, 0, -7836699, -22259015350]\) | \(-1680914269/5786802\) | \(-183238306749285095153664\) | \([2]\) | \(11980800\) | \(3.1498\) |
Rank
sage: E.rank()
The elliptic curves in class 170352.ev have rank \(0\).
Complex multiplication
The elliptic curves in class 170352.ev do not have complex multiplication.Modular form 170352.2.a.ev
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
